# Quadratic Equations - Real & Equal Roots

Ex 4.4 Q2. CBSE 10th Maths NCERT exercise solution

#### 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

##### i. 2x2 + kx + 3 = 0

The two roots of a quadratic equation ax2 + bx + c = 0 are real and equal if its discriminant b2 – 4ac = 0
In this equation a = 2, b = k and c = 3
∴ b2 – 4ac = k2 - 4 × 2 × 3 = 0
k2 - 24 = 0
k = ±$$sqrt{24}$ = ±2$\sqrt{6}$ ##### ii. kx$x - 2) + 6 = 0

kx2 – 2kx + 6 = 0
The two roots of a quadratic equation ax2 + bx + c = 0 are real and equal if its discriminant b2 – 4ac = 0
In this equation a = k, b = -2k and c = 6
∴ b2 - 4ac = (-2k)2 - 4 × k × 6 = 0
4k2 - 24k = 0
Divide the equation by 4: k2 - 6k = 0
k(k - 6) = 0
So k = 0 or k = 6
If k = 0 the quadratic equation will not exist.
∴ k = 6