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Solution - Find that non-zero value of k, for which the quadratic equation kx^2 + 1 − 2(k − 1)x + x^2 = 0 has equal roots. Hence find the roots of the equation. - CBSE Class 10 - Mathematics

ConceptNature of Roots

Question

Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.

Solution

We have

kx2 +12(k1)x+x2=0

This equation can be rearranged as

(k+1)x2 2(k1)x+1=0

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

∴ D = b2 − 4ac

=[2(k1)2]4×(k+1)×1

=4(k1)24(k+1)

=4[(k1)2 k1] 

=4[k2 +12kk1]

=4[k23k]

=4[k(k3)]

The given equation will have equal roots, if D = 0

⇒ 4[k(k−3)] = 0

k = 0 or − 3 = 0

k = 3

Putting k = 3 in the given equation, we get

4x24x+1=0 

(2x1)2=0

2x1=0

`=>x=1/2`

Hence, the roots of the given equation are `1/2 " and "1/2`

Is there an error in this question or solution?

Reference Material

Solution for question: Find that non-zero value of k, for which the quadratic equation kx^2 + 1 − 2(k − 1)x + x^2 = 0 has equal roots. Hence find the roots of the equation. concept: null - Nature of Roots. For the course CBSE
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