CA Foundation · Quantitative Aptitude · Equations
If x = 2 is a root of x³ − 3x² − 4x + 12 = 0, what are the other two roots?
The other roots are 3 and −2. Grouping gives x²(x − 3) − 4(x − 3) = (x − 3)(x − 2)(x + 2), so the roots are 3, 2 and −2. Since 2 is already given, the remaining two are 3 and −2.
- A3 and −2Correct
- B−3 and 2
- C3 and 4
- D−3 and −2
Explanation
Factorise by grouping: x²(x − 3) − 4(x − 3) = (x − 3)(x² − 4) = (x − 3)(x − 2)(x + 2). Roots are 3, 2 and −2. Given 2 is a root, the others are 3 and −2. Check: sum = 3 + 2 − 2 = 3 = −(−3)/1 and product = −12 = −12/1, which agrees.
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