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Find the values of k for each of the following quadratic equations, so that they have two equal roots. - Mathematics

Find the values of k for each of the following quadratic equations, so that they have two equal roots.

kx (x - 2) + 6 = 0

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Solution

kx(x - 2) + 6 = 0

or kx2 - 2kx + 6 = 0

Comparing this equation with ax2 + bx + c = 0, we get

a = k, b = - 2k and c = 6

Discriminant = b2 - 4ac

= ( - 2k)2 - 4 (k) (6)

= 4k2 - 24k

For equal roots,

b2 - 4ac = 0

4k2 - 24k = 0

4k (k - 6) = 0

Either 4k = 0 or k = 6 = 0

k = 0 or k = 6

However, if k = 0, then the equation will not have the terms 'x2' and 'x'.

Therefore, if this equation has two equal roots, k should be 6 only

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.4 | Q 2.2 | Page 91
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