Question

find the value of k for the quadratic equation k x^2+ ( 2k + 4 ) x+ 9 = 0 so that they have two equal roots

plz help me it's urgent yaar ​

Answer 1

Answer:

k = 1,4

Step-by-step explanation:

Given Equation is kx² + (2k + 4)x + 9 = 0

Comparing with ax² + bx + c = 0, we get

a = k, b = (2k + 4), c = 9

Since the equation has 2 equal roots.

D = 0

∴ b² - 4ac = 0

⇒ (2k + 4)² - 4(k)(9) = 0

⇒ 4k² + 16 + 16k - 36k = 0

⇒ 4k² + 16 - 20k = 0

⇒ 4k² - 20k + 16 = 0

⇒ k² - 5k + 4 = 0

⇒ k² - 4k - k + 4 = 0

⇒ k(k - 4) - (k - 4) = 0

⇒ (k - 1)(k - 4) = 0

⇒ k = 1,4

Hope it helps!