alleryThe solutions of the equation x² + 2x − 15 = 0 are:
A3 and 5
B3 and −5
C−3 and 5
D−3 and −5
Answer & Solution
Correct answer: C. −3 and 5
1. Write x² + 2x − 15 = (x − a)(x − b), requiring a + b = −2 and ab = −15.
2. Factor pairs of 15: 3 × 5. One must be negative since the product is negative.
3. Trying a = −3, b = 5: a + b = 2, ab = −15 — sum is wrong.
4. Trying a = 3, b = −5: a + b = −2, ab = −15 — both match.
5. So x² + 2x − 15 = (x − 3)(x + 5) and the solutions are 3 and −5.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
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