If p,q are zeroes of polynomials …
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Sia ? 6 years, 6 months ago
we have f(x) = 2x2 - 7x +3
{tex}\Rightarrow{/tex} Sum of roots = p + q = {tex}- \frac { \text { Coefficient of } x } { \text { Coefficient of } x ^ { 2 } }{/tex}
= {tex}- \left( \frac { - 7 } { 2 } \right) = \frac { 7 } { 2 }{/tex}
{tex}\Rightarrow{/tex} Product of roots = pq = {tex}{/tex}{tex}\frac { \text { Constant term } } { \text { Coefficient of } x ^ { 2 } } = \frac { 3 } { 2 }{/tex}
Since, {tex}(p+q)^2{/tex} = p2 + q2 + 2pq
{tex}\Rightarrow{/tex} 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 {tex}p^2+q^2{/tex}= {tex}\frac{37}{4}{/tex}
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