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CAT 2003 Slot 1 — QA Question 45

Domain & RangeEasy

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?

Answer & solution

Correct answer: The two curves intersect thrice

  • A

    The two curves intersect once

  • B

    The two curves intersect twice

  • C

    The two curves do not intersect

  • The two curves intersect thrice

Solution

y = x3 + x2 + 5                                     … (i)

y = x2 + x + 5                                      … (ii)

Solving (i) and (ii), we get,

x3 + x2 + 5 = x2 + x + 5

x(x2 − 1) = 0

∴ x = 0, 1, −1

∴ All three solutions for (i) and (ii) lie between −2 and 2.

∴ The two curves intersect thrice in the given range.

Hence, option (d).

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CAT 2003 Slot 1 QA Q45: Consider the following two curves in the X-Y plane y = x 3 + x 2 + 5 y = x 2 + x + 5 Which of the following st — Solution | TheCATExam