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(B) Given the quadratic equation $x^2 - 6x + a = 0$,the sum of the roots is $\alpha + \beta = 6$ and the product of the roots is $\alpha\beta = a$.Giv

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) Given the quadratic equation $x^2 - 6x + a = 0$,the sum of the roots is $\alpha + \beta = 6$ and the product of the roots is $\alpha\beta = a$.Given the relation $3\alpha + 2\beta = 16$,we can rewrite it as $2(\alpha + \beta) + \alpha = 16$.Substituting $\alpha + \beta = 6$ into the equation: $2(6) + \alpha = 16$ $\Rightarrow 12 + \alpha = 16$ $\Rightarrow \alpha = 4$.Since $\alpha + \beta = 6$,we have $4 + \beta = 6 \Rightarrow \beta = 2$.Now,using the product of the roots: $a = \alpha\beta = 4 	imes 2 = 8$.

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 6x + a = 0$ and satisfy the relation $3\alpha + 2\beta = 16$,then the value of $a$ is

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