Mia B.
asked 10/12/17The roots of f(x) are 3, 4, and 2. What are the roots of f(x^2+1)
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1 Expert Answer

Philip P. answered 10/12/17
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If the roots of f(x) are 3, 4, and 2, then:
f(x) = a(x-4)(x-3)(x-2)
where a is a non-zero constant. So:
f(x2+1) = a(x2+1-4)(x2+1-3)(x2+1-2)
f(x2+1) = a(x2-3)(x2-2)(x2-1)
The roots occur when f(x2+1) = 0:
0 = a(x2-3)(x2-2)(x2-1)
x = ±√3, ±√2, ±1
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Michael J.
10/12/17