Question

The solution set for the quadratic equation `2x^2 - x + 1/8 = 0` is ______.

Options

• `{1/4, 1/4}`

• `{-1/4, 1/4}`

• `{-1/2, 1/4}`

• {4, 4}

Answer 1

The solution set for the quadratic equation `2x^2 - x + 1/8 = 0` is `underlinebb({1/4, 1/4})`.

Explanation:

Given,

⇒ `2x^2 - x + 1/8 = 0`

Multiply the equation with 16, we get:

⇒ `16(2x^2 - x + 1/8 = 0)`

⇒ `32x^2 - 16x + 16/8 = 0`

⇒ 32x² – 16x + 2 = 0

⇒ 2(16x² – 8x + 1) = 0

⇒ 16x² – 8x + 1 = 0

⇒ 16x² – 4x – 4x + 1 = 0

⇒ 4x(4x – 1) – 1(4x – 1) = 0

⇒ (4x – 1)(4x – 1) = 0

⇒ (4x – 1) = 0 or (4x – 1) = 0   ...[Using zero-product rule]

⇒ 4x = 1 or 4x = 1

⇒ `x = 1/4` or `x = 1/4`