Question

Find value of K so that equation has two equal roots : (1+k^2)x^2 + 2kcx + (c^2 - a^2) = 0​

Answer 1

Answer:

Step-by-step explanation:

Explanation

In this question, we are asked to find the value of k for which the equation has two equal roots

The given equation is (1+k^2)x^2+2kcx+(c^2-a^2)=0

Theory

To find the value of k for which the given equation has 2 real roots, the value of the discriminant of the equation should be equal to 0

D= b^2-4ac=0

Solving

On solving and equating discriminant to 0

4k^2c^2 - 4(1+k^2)(c^2-a^2) = 0

4k^2c^2 - 4 ( c^2- a^2+k^2c^2 - k^2a^2)=0

On further solving this equation....

-4c^2 + 4a^2 + 4k^2a^2 = 0

4( a^2-c^2) = -4k^2a^2

- k^2= a^2 - c^2/a^2

Therefore

k= c^2 - a^2 / a^2