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?
Explanation:
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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