What is the nature of the roots of 2x² + 5x − 6 = 0?

Correct answer: Two different roots. The discriminant is b² − 4ac = 25 + 48 = 73, which is positive, so there are two different real roots.

Background: D > 0 gives two different real roots, D = 0 gives equal roots, and D < 0 gives no real roots.

• Two same roots: Two equal roots need a discriminant of zero.
• Both A & B: “Both A & B” is incorrect because only one option is true.
• None of these: “None of these” is incorrect because two different roots is correct.

Did you know? 73 is not a perfect square, so the roots are irrational.

Memory trick: D = 73 > 0 → two roots.