Question

Find the value of k for which the equation x^2 + 5kx+16=0 has real and equal roots

Answer 1

Answer:

Equation: x² + 5kx + 16 = 0

It is given that all the roots are equal.

For roots to be equal, the value of Discriminant must be equal to zero.

=> D = b² -4ac

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

=> D = ( 5k )² - 4 ( 1 ) ( 16 )

=> D = 25 k² - 64  

We know that D is equal to zero.

=> 25k² - 64 = 0

=> 25k² = 64

=> k² = 64 / 25

=> k = √ ( 64 / 25 )

=> k = + 8 / 5 ( or ) - 8 / 5

Hope it helped !

Answer 2

HEY There!!!


Question;-

Find the value of k for which the equation x^2 + 5kx+16=0 has real and equal roots



Method of Solution;-

We know that Discriminant = b²-4ac

For real and Equal roots So Discriminant must be 0

Now, Using Discriminant to solve this Question!!

x²+5kx +16 = 0

b²-4ac = 0

(5k)² -4 .1. 16 = 0

25k² -64 = 0

25k²= 64

k² = 64/25

•°• k = ±√ 64/ √ 25

•°• k = ± 8/5

Hence, K = ±8/5