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

(i) 2x^{2} + kx + 3 = 0 (ii) kx (x - 2) + 6 = 0

**Solution:**

If a quadratic equation ax^{2} + bx + c = 0, then it has equal real roots. So, discriminant b^{2} - 4ac = 0

(i) 2x^{2} + kx + 3 = 0

a = 2, b = k, c = 3

b^{2} - 4ac = 0

(k)^{2} - 4(2)(3) = 0

k^{2} - 24 = 0

k^{2} = 24

k = √24

k = ± √2 × 2 × 2 × 3

k = ± 2√6

(ii) kx (x - 2) + 6 = 0

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

b^{2} - 4ac = 0

(-2k)^{2} - 4(k)(6) = 0

4k² - 24k = 0

4k (k - 6) = 0

k = 6 and k = 0

If we consider the value of k as 0, then the equation will no longer be quadratic.

Therefore, k = 6

**Video Solution:**

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

### Class 10 Maths NCERT Solutions - Chapter 4 Exercise 4.4 Question 2:

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

The value of k such that each quadratic equation has two equal roots is (i) ± 2√6 and (ii) k = 6.