In the following question, two statements (i) and (ii) are given. Choose the valid statement. i. The equation x2 – 6x – 7 = 0 has no real root. ii. The equation 4x2 – 6x + 1 = 0 has equal roots.

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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.

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