Question

If sum of the squares of zeroes of the quadratic polynomial f(x)=x square -8x+k is 40. find value of k​

Answer 1

Answer:

f(x) = x² - 8x + k

sum of its zeros is 40

let its zeros to be= alpha and beta

GIVEN THAT, ALPHA² +BETA² = 40

alpha²+ beta² +2alpha × beta - 2alpha×beta = 40

[ alpha² + beta² + 3alpha× beta ] - 2alpha × beta =40

[alpha +beta]²- 2alpha x beta =40 ----------- equation. 1

from the equation, alpha +beta = -b/a = -1/-8

= 1/8

and, alpha x beta = c/a = k/-8

put these values in eq.1

(1/8)² - 2 x k/-8 = 40

1/64 + k/4 = 40

64 + 16k/64 = 40

64 + 16k = 64 x 40

16k = 2560

k = 2560/16 = 156

HENCE THE VALUE OF k IS 156.

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