Question

Solve the quadratic equation 8x² – 14x + 3 = 0

1. When x ∈ I (integers)
2. When x ∈ Q (rational numbers)

Answer 1

Given quadratic equation is 8x² – 14x + 3 = 0

`=>` 8x² – 12x – 2x + 3 = 0

`=>` 4x(2x – 3) – (2x – 3) = 0

`=>` (2x – 3)(4x – 1) = 0

`=>` (2x – 3) = 0 or (4x – 1) = 0

`=> x = 3/2` or `x = 1/4`

i. When x ∈ I the equation 8x² – 14x + 3 = 0 has no roots

ii. When x ∈ Q the roots of 8x² – 14x + 3 = 0 are

x = `3/2` or x = `1/4`