Question

Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(i) 2x2 + kx + 3 = 0
(ii) kx (x – 2) + 6 = 0

Answer 1

(i) 2x² + kx + 3 = 0

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

a = 2, b = k and c = 3

As we know, Discriminant = b² – 4ac

= (k)² – 4(2) (3)

= k² – 24

For equal roots, we know,

Discriminant = 0

k² – 24 = 0

k² = 24

k = ±√24 = ±2√6

(ii) kx(x – 2) + 6 = 0

or kx² – 2kx + 6 = 0

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

a = k, b = – 2k and c = 6

We know, Discriminant = b² – 4ac

= ( – 2k)2 – 4 (k) (6)

= 4k² – 24k

For equal roots, we know,

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.

Answer 2

( ‘x2‘ and ‘x‘.

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