Product of Distinct Roots of Absolute Quadratic

CAT 2019 Slot 1 · Quantitative Ability · Medium · Quadratic equations

This is a medium Quantitative Ability question from the CAT 2019 Slot 1 paper. It tests Quadratic equations. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2019 Slot 1 questions More Quadratic equations questions All CAT QA

The product of the distinct roots of $|x^2 - x - 6| = x + 2$ is

A.
-4
B.
-16
C.
-8
D.
-24

Answer

Explanation

Note $|x^2 - x - 6| = |(x-3)(x+2)| = x + 2$ . Case 1: $x + 2 < 0 \implies x < -2$ : No real solution since LHS $\ge 0$ . Case 2: $x = -2$ : LHS $= 0 =$ RHS, so $x = -2$ is a solution. Case 3: $x > -2$ : $x+2 > 0$ , so we divide both sides by $x+2$ . $|x - 3| = 1 \implies x - 3 = 1$ or $x - 3 = -1 \implies x = 4$ or $x = 2$ . Both $4$ and $2$ are $> -2$ . Distinct roots are $-2, 2, 4$ . Product $= (-2) \times 2 \times 4 = -16$ .

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace

Product of Distinct Roots of Absolute Quadratic

Explanation

Related Quadratic equations questions

Practise this under exam conditions