Question

Choose the correct answer from the given four options :

If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is

Options

• ${\displaystyle \frac{9}{8}}$

• ${\displaystyle -\frac{9}{8}}$

• ${\displaystyle \frac{1}{8}}$

• ${\displaystyle -\frac{1}{8}}$

Answer 1

2x² – 5x + (k + 3) = 0
a = 2, b = –5, c = k + 3
∴ b² – 4ac
= (–5)² – 4 x 2 x (k + 3)
= 25 – 8(k + 3)
∴ Roots are equal.
∴ b² – 4ac = 0
∴ 25 – 8(k + 3) = 0
25 – 8k - 24 = 0
1 – 8k = 0
⇒ 8k = 1

∴ k = ${\displaystyle \frac{1}{8}}$.