Question

If the following equation has two equal and real roots then find the value of K ?

$x {}^{2} + 2x + k(3x {}^{2} + 2x + 1) = 0$
( Non-sense answers will be deleted on the spot ! )

( Clear answers expected ! )

Answer 1

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

Comparing Equation with ax^2 + bx + c = 0

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

Given that the equation has two equal roots.

D = 0

b^2 - 4ac = 0


On substituting the values, we get

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

4 - 4k = 0

4 = 4k

k = 1.

Answer 2

=======. *******

ax^2 + bx + c = 0

a = 1, b = 2, c = k

(3x^2 + 2x + 1)




------__. equation has two equal roots. ------. _

D = 0

b^2 - 4ac = 0




================, we get

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

4 - 4k = 0

4 = 4k

k = 1.