Question

What will be the value of k, if the roots of the equation (k – 4)x^2 – 2kx + (k + 5) = 0 are equal?

(a) 18

(b) 19

(c) 20

(d) 21

The question was asked in unit test.

Question is taken from Quadratic Equation in chapter Quadratic Equation of Mathematics – Class 10

Answer 1

Correct answer is (c) 20

For explanation: Roots are equal. ∴ b^2 – 4ac = 0

-(2k)^2 – 4(k – 4)(k + 5) = 0

4k^2 – 4(k^2 – 4k + 5k – 20) = 0

4k^2 – 4(k^2 + k – 20) = 0

4k^2 – 4k^2 – 4k + 80 = 0

-4k =  – 80

k = \(\frac {-80}{-4}\) = 20