Question

find the value of k such that the sum of squares of the roots of the equation x^2-8x+k=0 and alpha square and beta square =40​

Answer 1

Given:x²-8x+k=0

α²+β²=40

We know that

Sum of zeroes= -  coefficient of x/coefficient of x²

α+β= -(-8/1)

α+β = 8

Product of zeroes= constant term/coefficient of x²

αβ= k

Also,

α²+β²=(α+β)²-2αβ

Putting the values

40=(8)²-2k

40=64-2k

2k=64-40

2k=24

k=12

Hence, value of k=12

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