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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»

\LARGE\underline{\underline{\textsf{\textbf{Given\::-}}}}

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  • Sum of zeroes of quadratic polynomial (S) = 9/2

  • Product of zeroes of a quadratic polynomial (P) = 2

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\LARGE\underline{\underline{\textsf{\textbf{To\:Find\::-}}}}

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  • Quadratic polynomial ?

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\LARGE\underline{\underline{\textsf{\textbf{Solution\::-}}}}

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  • We CLEARLY know that, for finding a quadratic polynomial with sum of zeroes = S, and product of zeroes = P, we USE equation ::

  • \Large\boxed{\bf{p(<klux>X</klux>) = x^2 - Sx + P}}

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\underline{\sf{\bigstar\:Putting\:all\:known\:values\:::}}

\\ \quad \longrightarrow \quad \sf p(x) = x^2 - \bigg(\dfrac{9}{2}\bigg)x + 2

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\underline{\sf{\bigstar\:Multiplying\:the\:equation\:with\:2\:::}}

\\ \quad \longrightarrow \quad \sf p(x) = 2\Bigg(x^2 - \bigg(\dfrac{9}{2}\bigg)x + 2\Bigg)

\\ \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)

\\ \quad \longrightarrow \quad \large \bf p(x) = 2x^2 - 9x + 4

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\therefore\:{\underline{\sf{Hence,\:required\:polynomial\:is\:\bf{2x^2 - 9x + 4}}}}

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\LARGE\underline{\underline{\textsf{\textbf{Explore\:More\::-}}}}

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  • If α and β are zeroes of the quadratic polynomial ax² + bx + c, then α + β = -b/a and αβ = c/a.

  • If α, β, γ are the zeroes of cubic polynomial ax³ + bx² + cx + d, then α + β + γ = -b/a, αβ + βγ + γα = c/a and αβγ = -d/a.

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\LARGE\underline{\underline{\textsf{\textbf{Learn\:more\:on\:brainly\::-}}}}

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\underline{\sf{\bigstar\:Question\:::}}

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Find zeroes of the quadratic polynomial 4x² - x - 5 and verify RELATIONSHIP between it's zeroes and coefficients.

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\underline{\sf{\bigstar\:Answer\:::}}

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brainly.in/question/42964609

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