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Please Help Me !Chapter-Quadratic Polynomial Find a quadratic polynomial whose sum of zeros is 9 / 2 and product of zeros is 2 |
| Answer» <html><body><p><img align="absmiddle" alt="\LARGE\underline{\underline{\textsf{\textbf{Given\::-}}}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%5CLARGE%5Cunderline%7B%5Cunderline%7B%5Ctextsf%7B%5Ctextbf%7BGiven%5C%3A%3A-%7D%7D%7D%7D" title="\LARGE\underline{\underline{\textsf{\textbf{Given\::-}}}}"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><ul><li>Sum of zeroes of quadratic polynomial (S) = <strong>9/2</strong></li></ul><p></p><ul><li>Product of zeroes of a quadratic polynomial (P) = <strong>2</strong></li></ul><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\LARGE\underline{\underline{\textsf{\textbf{To\:Find\::-}}}}" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%5CLARGE%5Cunderline%7B%5Cunderline%7B%5Ctextsf%7B%5Ctextbf%7BTo%5C%3AFind%5C%3A%3A-%7D%7D%7D%7D" title="\LARGE\underline{\underline{\textsf{\textbf{To\:Find\::-}}}}"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><ul><li>Quadratic polynomial ?</li></ul><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\LARGE\underline{\underline{\textsf{\textbf{Solution\::-}}}}" class="latex-formula" id="TexFormula7" src="https://tex.z-dn.net/?f=%5CLARGE%5Cunderline%7B%5Cunderline%7B%5Ctextsf%7B%5Ctextbf%7BSolution%5C%3A%3A-%7D%7D%7D%7D" title="\LARGE\underline{\underline{\textsf{\textbf{Solution\::-}}}}"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula8" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><ul><li>We <a href="https://interviewquestions.tuteehub.com/tag/clearly-420736" style="font-weight:bold;" target="_blank" title="Click to know more about CLEARLY">CLEARLY</a> know that, for finding a quadratic polynomial with sum of zeroes = <strong>S</strong>, and product of zeroes = <strong>P</strong>, we <a href="https://interviewquestions.tuteehub.com/tag/use-1441041" style="font-weight:bold;" target="_blank" title="Click to know more about USE">USE</a> equation :: </li></ul><p></p><ul><li><img align="absmiddle" alt="\Large\boxed{\bf{p(<klux>X</klux>) = x^2 - Sx + P}}" class="latex-formula" id="TexFormula9" src="https://tex.z-dn.net/?f=%5CLarge%5Cboxed%7B%5Cbf%7Bp%28x%29%20%3D%20x%5E2%20-%20Sx%20%2B%20P%7D%7D" title="\Large\boxed{\bf{p(x) = x^2 - Sx + P}}"/></li></ul><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula10" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\underline{\sf{\bigstar\:Putting\:all\:known\:values\:::}}" class="latex-formula" id="TexFormula11" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Csf%7B%5Cbigstar%5C%3APutting%5C%3Aall%5C%3Aknown%5C%3Avalues%5C%3A%3A%3A%7D%7D" title="\underline{\sf{\bigstar\:Putting\:all\:known\:values\:::}}"/></p><p></p><p><img align="absmiddle" alt="\\ \quad \longrightarrow \quad \sf p(x) = x^2 - \bigg(\dfrac{9}{2}\bigg)x + 2" class="latex-formula" id="TexFormula12" src="https://tex.z-dn.net/?f=%5C%5C%20%5Cquad%20%5Clongrightarrow%20%5Cquad%20%5Csf%20p%28x%29%20%3D%20x%5E2%20-%20%5Cbigg%28%5Cdfrac%7B9%7D%7B2%7D%5Cbigg%29x%20%2B%202%20" title="\\ \quad \longrightarrow \quad \sf p(x) = x^2 - \bigg(\dfrac{9}{2}\bigg)x + 2"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula13" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\underline{\sf{\bigstar\:Multiplying\:the\:equation\:with\:2\:::}}" class="latex-formula" id="TexFormula14" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Csf%7B%5Cbigstar%5C%3AMultiplying%5C%3Athe%5C%3Aequation%5C%3Awith%5C%3A2%5C%3A%3A%3A%7D%7D" title="\underline{\sf{\bigstar\:Multiplying\:the\:equation\:with\:2\:::}}"/></p><p></p><p><img align="absmiddle" alt="\\ \quad \longrightarrow \quad \sf p(x) = 2\Bigg(x^2 - \bigg(\dfrac{9}{2}\bigg)x + 2\Bigg)" class="latex-formula" id="TexFormula15" src="https://tex.z-dn.net/?f=%5C%5C%20%5Cquad%20%5Clongrightarrow%20%5Cquad%20%5Csf%20p%28x%29%20%3D%202%5CBigg%28x%5E2%20-%20%5Cbigg%28%5Cdfrac%7B9%7D%7B2%7D%5Cbigg%29x%20%2B%202%5CBigg%29%20" title="\\ \quad \longrightarrow \quad \sf p(x) = 2\Bigg(x^2 - \bigg(\dfrac{9}{2}\bigg)x + 2\Bigg)"/></p><p></p><p><img align="absmiddle" alt="\\ \quad \longrightarrow \quad \sf p(x) = \big(2\:\times\:x^2\big) - \bigg(\dfrac{9}{\cancel{2}}\:\times\:\cancel{2}\bigg)x + \big(2\:\times\:2\big)" class="latex-formula" id="TexFormula16" src="https://tex.z-dn.net/?f=%5C%5C%20%5Cquad%20%5Clongrightarrow%20%5Cquad%20%5Csf%20p%28x%29%20%3D%20%5Cbig%282%5C%3A%5Ctimes%5C%3Ax%5E2%5Cbig%29%20-%20%5Cbigg%28%5Cdfrac%7B9%7D%7B%5Ccancel%7B2%7D%7D%5C%3A%5Ctimes%5C%3A%5Ccancel%7B2%7D%5Cbigg%29x%20%2B%20%5Cbig%282%5C%3A%5Ctimes%5C%3A2%5Cbig%29" title="\\ \quad \longrightarrow \quad \sf p(x) = \big(2\:\times\:x^2\big) - \bigg(\dfrac{9}{\cancel{2}}\:\times\:\cancel{2}\bigg)x + \big(2\:\times\:2\big)"/></p><p></p><p><img align="absmiddle" alt="\\ \quad \longrightarrow \quad \large \bf p(x) = 2x^2 - 9x + 4" class="latex-formula" id="TexFormula17" src="https://tex.z-dn.net/?f=%5C%5C%20%5Cquad%20%5Clongrightarrow%20%5Cquad%20%5Clarge%20%5Cbf%20p%28x%29%20%3D%202x%5E2%20-%209x%20%2B%204" title="\\ \quad \longrightarrow \quad \large \bf p(x) = 2x^2 - 9x + 4"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula18" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\therefore\:{\underline{\sf{Hence,\:required\:polynomial\:is\:\bf{2x^2 - 9x + 4}}}}" class="latex-formula" id="TexFormula19" src="https://tex.z-dn.net/?f=%5Ctherefore%5C%3A%7B%5Cunderline%7B%5Csf%7BHence%2C%5C%3Arequired%5C%3Apolynomial%5C%3Ais%5C%3A%5Cbf%7B2x%5E2%20-%209x%20%2B%204%7D%7D%7D%7D" title="\therefore\:{\underline{\sf{Hence,\:required\:polynomial\:is\:\bf{2x^2 - 9x + 4}}}}"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula20" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\LARGE\underline{\underline{\textsf{\textbf{Explore\:More\::-}}}}" class="latex-formula" id="TexFormula21" src="https://tex.z-dn.net/?f=%5CLARGE%5Cunderline%7B%5Cunderline%7B%5Ctextsf%7B%5Ctextbf%7BExplore%5C%3AMore%5C%3A%3A-%7D%7D%7D%7D" title="\LARGE\underline{\underline{\textsf{\textbf{Explore\:More\::-}}}}"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula22" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><ul><li>If<strong> </strong><strong>α</strong> and <strong>β</strong><strong> </strong>are zeroes of the quadratic polynomial <strong>a</strong><strong>x</strong><strong>²</strong><strong> </strong><strong>+</strong><strong> </strong><strong>b</strong><strong>x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>c</strong><strong>,</strong><strong> </strong>then <strong>α + β = -b/a</strong><strong> </strong>and<strong> </strong><strong>αβ = c/</strong><strong>a</strong><strong>.</strong></li></ul><p></p><ul><li>If<strong> </strong><strong>α</strong><strong>,</strong><strong> </strong><strong>β</strong><strong>,</strong><strong> </strong><strong>γ</strong><strong> </strong>are the zeroes of cubic polynomial <strong>a</strong><strong>x</strong><strong>³</strong><strong> </strong><strong>+</strong><strong> </strong><strong>b</strong><strong>x</strong><strong>²</strong><strong> </strong><strong>+</strong><strong> </strong><strong>c</strong><strong>x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>d</strong><strong>,</strong><strong> </strong>then <strong>α + β + γ = -b/a</strong><strong>,</strong><strong> </strong><strong>αβ + βγ + γα = c/</strong><strong>a</strong><strong> </strong>and <strong>αβγ</strong><strong> </strong><strong>=</strong><strong> </strong><strong>-</strong><strong>d</strong><strong>/</strong><strong>a</strong><strong>.</strong></li></ul><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula23" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\LARGE\underline{\underline{\textsf{\textbf{Learn\:more\:on\:brainly\::-}}}}" class="latex-formula" id="TexFormula24" src="https://tex.z-dn.net/?f=%5CLARGE%5Cunderline%7B%5Cunderline%7B%5Ctextsf%7B%5Ctextbf%7BLearn%5C%3Amore%5C%3Aon%5C%3Abrainly%5C%3A%3A-%7D%7D%7D%7D" title="\LARGE\underline{\underline{\textsf{\textbf{Learn\:more\:on\:brainly\::-}}}}"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula25" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\underline{\sf{\bigstar\:Question\:::}}" class="latex-formula" id="TexFormula26" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Csf%7B%5Cbigstar%5C%3AQuestion%5C%3A%3A%3A%7D%7D" title="\underline{\sf{\bigstar\:Question\:::}}"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula27" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p>Find zeroes of the quadratic polynomial 4x² - x - 5 and verify <a href="https://interviewquestions.tuteehub.com/tag/relationship-1183331" style="font-weight:bold;" target="_blank" title="Click to know more about RELATIONSHIP">RELATIONSHIP</a> between it's zeroes and coefficients.</p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula28" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><img align="absmiddle" alt="\underline{\sf{\bigstar\:Answer\:::}}" class="latex-formula" id="TexFormula29" src="https://tex.z-dn.net/?f=%5Cunderline%7B%5Csf%7B%5Cbigstar%5C%3AAnswer%5C%3A%3A%3A%7D%7D" title="\underline{\sf{\bigstar\:Answer\:::}}"/></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula30" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><a class="sg-link" href="https://brainly.in/question/42964609">brainly.in/question/42964609</a></p><p><img align="absmiddle" alt="\:" class="latex-formula" id="TexFormula31" src="https://tex.z-dn.net/?f=%5C%3A" title="\:"/></p><p><u>━━━━━━━━━━━━━━━━━━━━━━━━</u><u>━</u></p></body></html> | |