Question

If alpha and beta are zeroes of x2-8+k such that alpha square + beta square =40 ,find k

Answer 1

Answer:

$k =12$

Step-by-step explanation :

$\alpha +\beta = 8$

( The sum of roots is $-\frac{b}{a}$ )

$\alpha \beta =k$

( The product of roots is  $\frac{c}{a}$ )

And so,

$(\alpha +\beta )^{2} = 8^{2} \\\\alpha ^{2} +2\alpha \beta +\beta ^{2} = 64\\\ \alpha ^{2} +\beta^{2} +2\alpha \beta =64$

Substitute $\alpha ^{2} +\beta^{2} = 40, \alpha\beta = k$ into the equation,

$40+2k =64\\k = 12$

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