Question

find K so that the quadratic equation (k+1)x^2 -2(k+1)x+1=0 has equal roots

Answer 1

in quadratic equation roots are equal if discrimination (D)=0
b^2-4ac=0
or [-2(k+1)]^2-4(k+1)(1)=0
or 4(k+1)^2-4(k+1)=0
or 4(k+1)[k+1-1]=0
or 4k(k+1)=0
or k= 0, -1 answer.

Answer 2

The value of k will be 1 or 0.

Given,

A quadratic equation (k+1)x² -2(k+1)x+1=0.

To Find,

The value of k such that the equation has equal roots.

Solution,

For a quadratic equation to have equal roots the value of the discriminant must be equal to 0.

So,

D = b²-4ac = 0

In the given equation

b = -2(k+1), a = (k+1), and c = 1

So,

(-2(k+1))²-4(k+1)(1) = 0

4(k²+1+2k) = 4k+4

4k²+4+8k = 4k+4

4k² = -4k

k²-k = 0

k(k-1) = 0

k = 1 or 0.

Hence, the value of k is 1 or 0.