Question

Find the value(s) of k for which the equation has x2+15kx+16=0 has real and equal roots

Answer 1

Answer:

k = 8/15

Step-by-step explanation:

x² + 15kx + 16 = 0

It has real and equal roots

⇒ b²  - 4ac = 0

Solve k:

b²  - 4ac = 0

(15k)²  - 4(1)(16) = 0

225k² - 64 = 0

225k² = 64

k² = 64/225

k = √(64/225)

k = 8/15

Answer: k = 8/15

Answer 2

Answer: k = 8 /15

Step-by-step explanation:

Given : quadratic equation  = x² + 15 kx + 16 = 0

in which a = 1 , b = 15 k , c = 16

since there are no real roots

b² - 4ac < 0

That is

( 15k) ² - 4 (1) (16) < 0

225 k² - 64 < 0

k² < 64 /225

k < √ 64/225

k < 8/ 15

Hence k = 8 /15