Question

if the sum of the square of the zeros of the polynomial 6 X square + X + K is 25 / 36 find the value of k

Answer 1

$6 {x}^{2} + x + k = 0 \\ let \: roots \: be \: \alpha \: and \: \beta \\now \: from \: eqn \: \\ \alpha + \beta = - 1 \div 6 \\ \alpha \beta = k \div 6 \\ given \\ { \alpha }^{2} + { \beta }^{2 } = 25 \div 36 \\ \\ ( \alpha + \beta ) {}^{2} - 2( \alpha \beta ) = 25 \div 36 \\ put \: values \: \\ ( - 1 \div 6) {}^{2} - 2(k \div 6) = 25 \div 36 \\ - 2(k \div 6) =( 25 \div 36) - (1 \div 36) \\ - (k \div 3) = 24 \div 36 \\ k = - (2)$
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