Multiple choice

Consider the following two curves in the x-y plane:

y = x3 + x2 + 5 y = x2 + x + 5

Which of the following statements is true for - 2 ≤ x ≤ 2?

  1. The two curves intersect once

  2. The two curves intersect twice

  3. The two curves do not intersect

  4. The two curves intersect thrice

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Curve I: y = x3 + x2 + 5

Curve II: y = x2 + x + 5
Range: -2 ≤ x ≤ 2
At x = 0            For curve I: y = 5
                        For curve II: y = 5
At x = 1 for curve I: y = 7
                        For curve II: y = 7
At x = -1 for curve I: y = (-1) + 1 + 5 = 5
                        For curve II: y = 1 + (-1) + 5 = 5 The curves y = x3 + x2 + 5 and y = x2 + x + 5 intersect in 3 at least points i.e., (0, 5), (1, 7) and (-1, 5).