If x² + x − 12 = 0, values of x will be:

Question

If x² + x − 12 = 0, values of x will be:

1. A. −3, 4
2. B. 3, −4 (Correct answer)
3. C. −3, −4
4. D. 3, 4

Correct Answer

Option B — 3, −4

Detailed Solution & Explanation

The correct answer is 3, −4.

Key Points

• Factorise x² + x − 12 by finding two numbers whose product is −12 and whose sum is +1: those are +4 and −3.
• So x² + x − 12 = (x + 4)(x − 3) = 0, giving x = −4 or x = 3.
• Substituting back confirms both: 9 + 3 − 12 = 0 and 16 − 4 − 12 = 0.

Additional Information

• For ax² + bx + c = 0, the sum of the roots is −b/a and the product is c/a — here sum = −1 and product = −12, which 3 and −4 satisfy.
• The quadratic formula x = [−b ± √(b² − 4ac)] / 2a always works when factorisation is not obvious.
• The discriminant b² − 4ac tells you the nature of the roots: positive gives two real roots, zero a repeated root, negative a complex pair.