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If sum of square of zeroes of quadratic polynomial f(x) x2-8x+k is 40 then find the value of k

Posted by Aman Singhal 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let {tex}\alpha,\beta{/tex} be the zeros of the polynomial {tex}f(x)=x^2-8x+k{/tex}.
Sum of zeroes = {tex} \alpha + \beta = - \left( \frac { - 8 } { 1 } \right) = 8{/tex} and, Product of zeroes = {tex} \alpha \beta = \frac { k } { 1 } = k{/tex}
Now,
{tex} \alpha ^ { 2 } + \beta ^ { 2 } = 40{/tex}

{tex} \Rightarrow \alpha ^ { 2 } + \beta ^ { 2 }+2 \alpha\beta-2 \alpha\beta= 40{/tex}
{tex} \Rightarrow \quad ( \alpha + \beta ) ^ { 2 } - 2 \alpha \beta = 40{/tex}
{tex} \Rightarrow \quad 8 ^ { 2 } - 2 k = 40{/tex}
{tex} \Rightarrow \quad 2 k = 64 - 40 {/tex}

{tex}\Rightarrow 2 k = 24 {/tex}

{tex}\Rightarrow k = 12{/tex}

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