Question

In the following question, two statements (i) and (ii) are given. Choose the valid statement.

1. The equation x² – 6x – 7 = 0 has no real root.
2. The equation 4x² – 6x + 1 = 0 has equal roots.

विकल्प

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Neither (i) nor (ii)

Explanation:

For x² − 6x − 7 = 0, the discriminant is 

Δ = (−6)² − 4(1) (−7)

= 36 + 28

= 64 > 0

So the equation has two real roots, not “no real root”. 

Statement (i) is false.

For 4x² − 6x + 1 = 0, the discriminant is

Δ = (−6)² − 4(4) (1)

= 36 − 16

= 20 > 0

So the roots are real and distinct, not equal.

Statement (ii) is false.