Question

Find the value of k for which the quadratic equation
kx² - 2√5x+4 = 0 has equal roots​

Answer 1

Given :- kx² - 2√5x+4 = 0 has equal roots

To find :- Find the value of k ?

Solution :- If the equation has two real and equal roots then , Discriminant = 0

−4ac=0

☘ Equation :- kx² - 2√5x + 4

where,

a = k

b = - 2√5

c = 4

b² - 4ac = 0

➛ (-2√5)² - 4 × k × 4 = 0

➛ 4 × 5 - 16k = 0

➛ 20 - 16k = 0

➛ - 16k = -20

➛ k = 20/16

➛ k = 5/4

Hence,

Value of k is 5/4Now,

Equation :- kx² - 2√5x + 4

⚘ Putting value of k.

➛ 5/4x² - 2√5x + 4

➛ (5x² - 8√5x + 16)/4

➛ 6x² - 8√5x + 16

Now,

Finding roots of the equation :- 6x² - 8√5x + 16 By Middle term splitting method .

➛ 5x² - 8√5x + 16

➛ 5x² - 4√5 - 4√5 + 16

➛ √5x(√5x - 4) -4(√5 - 4)

➛ (√5x - 4)(√5x -4)

➛ √5x - 4 = 0

➛ x = 4/√5 or x = 4/√5

hence ,

The roots are 4/√5 and 4/√5

Hope it helps_❤️