Determine the positive values of `' k '` for which the equation `x^2+k x+64=0` and `x^2-8x+k=0` will both have real roots.

Options

A. 4
B. 8
C. 12
D. 16

Answer

D

Explanation

(d) Given equations are `x^(2) + kx + 64 = 0`
and `x^(2) - 8x + k = 0`
since both the eqns have real roots, discriminant
` rArr b^(2) ge 4ac`
from `eq^(n) `(i) , we have
` k^(2) ge4(64) rArr k^(2) ge 256`
` rArr kge 16 `
and from `eq^(n)` (ii), we have
`rArr 64 ge 4k rArr 4 k le 64`
`rArr k ge 16 `
Hence, from eq^(n) (A) and (B), we have
`k=16`