Question

if alpha , beta are the two zeroes of the quadratic polynomial x^2 - 8x + k and (alpha)^2 + (beta)^2 = 40 find the value of k.

Answer 1

∵ α & β are zeroes

∴ α + β = -b/a

α.β=c/a

in p(x)= x² - 8x + k

a=1; b=-8; c=k

∴ α + β = -(-8)/1 = 8 ................................... (i)

α.β= k/1 = k .................................................(ii)

Squaring eq. (i)

(α + β)² = 8²

α² + β² + 2αβ = 64

40 + 2αβ = 64 .......................................................(∵ Given α²+β²=40)

2αβ = 24

αβ = 12

From eq(ii)

k = 12

HOPE IT HELPS.......................... :)

Answer 2

Hope it is correct.......