Mathematics

If y = x(^2) – x – 12, find the range of values of x…

If y = x(^2) – x – 12, find the range of values of x for which y ( geq ) 0

  • A.
    x 4
  • B.
    x ( leq ) -3 or x ( geq ) 4
  • C.
    -3
  • D.
    -3 ( leq ) x ( leq ) 4
Correct Answer: Option B
Explanation

y = x(^2) – x – 12
= (x – 4)(x + 3)
∴ x = 4 or x = -3
Checking the cases for y ( geq ) 0
We check values on the range x – 4 (geq) 0; x + 3 (leq) 0; x – 4 (leq) 0 and x + 3 (geq) 0 for the range which satisfies the inequality x(^2) – x – 12 (geq) 0.

We find that the inequality is satisfied on the range x (leq) -3 and x (geq) 4.