Question

Find the value(s) of k for which the equation x2 + 5kx + 16 = 0 has real and equal roots.

Answer 1

Hey

Here is your answer,

From the given equation x^2 + 5kx + 16 = 0

a = 1 , b = 5k , c = 16

b^2 - 4ac = 0

25k^2 - 4(1)(16) = 0

25k^2 = 64

k^2 = 64/25

K = 8/5

Hope it helps you!

Answer 2

For real and equal roots:-

$b^2=4ac$

$\implies (5k)^2=4*1*16$

$\implies 25k^2=64$

$\implies k^2=\frac{64}{25}$

$\implies k=\pm \frac {8}{5}$

k is either $\frac{8}{5}$

or k=$-\frac{8}{5}$

Thats your answer.

Hope it helps.