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If p, q are zeroes of polynomial p(x) = 2x2-7x+3, find the value of p2 + q2. |
| Answer» According to the question,\xa0p and q are the zeroes of polynomial f(x) = 2x2 - 7x + 3,\xa0f(x) = 2x2\xa0-7x + 3Sum of roots = p + q =\xa0{tex}- \\frac { \\text { Coefficient of } x } { \\text { Coefficient of } x ^ { 2 } }{/tex}{tex}= - \\left( \\frac { - 7 } { 2 } \\right) = \\frac { 7 } { 2 }{/tex}Product of roots= pq\xa0{tex}= \\frac { \\text { Constant term } } { \\text { Coefficient of } x ^ { 2 } } = \\frac { 3 } { 2 }{/tex}Since, (p + q)2\xa0=p2 + q2 + 2pqSo, p2 + q2 = (p + q)2 - 2pq{tex}= \\left( \\frac { 7 } { 2 } \\right) ^ { 2 } - 3 = \\frac { 49 } { 4 } - \\frac { 3 } { 1 } = \\frac { 37 } { 4 }{/tex}Hence, the value of p2+ q2={tex}\\frac{37}{4}{/tex} | |