Question

I need ans for this in detailed form plzz

Answer 1

Given Equation is (3k + 1)x^2 + 2(k + 1)x + k = 0.

On comparing with ax^2 + bx + c = 0, we get

a = (3k + 1), b = 2(k + 1), c = k.

Now,

Given that The Equation has real roots.

b^2 - 4ac = 0

(2(k + 1))^2 - 4(3k + 1)(k) = 0

4(k^2 + 1 + 2k) - 4(3k^2 + k) = 0

4k^2 + 4 + 8k - 12k^2 - 4k = 0

-8k^2 + 4k + 4 = 0

-2k^2 + k + 1 = 0

-2k^2 - 1k + 2k + 1 = 0

-k(2k + 1) + 1(2k + 1) = 0

(-k + 1)(2k + 1) = 0

(-k + 1) = 0 (or) (2k + 1) = 0

k = 1 (or) k = -1/2.


Hope this helps!