Question
Download Solution PDFComprehension
Directions: Read the following information and answer the three items that follow:
Let f(x) = x2 + 2x – 5 and g(x) = 5x + 30
What are the roots of the equation g[f(x)] = 0?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If α and β are the roots of the equation f(x) = ax2 + bx + c = 0. Then f(α) = 0 = f(β).
Calculation:
Given: f(x) = x2 + 2x – 5 and g(x) = 5x + 30
⇒ g[f(x)] = g(x2 + 2x – 5) = 5 (x2 + 2x – 5) + 30 = 5x2 + 10x + 5 = 0.
⇒ 5x2 + 10x + 5 = 0
⇒ x2 + 2x + 1 = (x + 1)2 = 0
⇒ x = - 1, -1
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