The value of k for which the roots alpha, bet | vedclass

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(D) Given the quadratic equation $x^{2}-6x+k=0$,the sum of the roots is $\alpha+\beta = -(-6)/1 = 6$.We are given the relation $3\alpha+2\beta=20$.Fro

Vedclass · Accepted Answer

$-16$

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(D) Given the quadratic equation $x^{2}-6x+k=0$,the sum of the roots is $\alpha+\beta = -(-6)/1 = 6$.We are given the relation $3\alpha+2\beta=20$.From the first equation,$\beta = 6-\alpha$. Substituting this into the second relation:$3\alpha + 2(6-\alpha) = 20$$3\alpha + 12 - 2\alpha = 20$$\alpha = 8$.Then,$\beta = 6 - 8 = -2$.The product of the roots is $\alpha\beta = k$.Therefore,$k = (8)(-2) = -16$.

The value of $k$ for which the roots $\alpha, \beta$ of the equation $x^{2}-6x+k=0$ satisfy the relation $3\alpha+2\beta=20$ is:

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