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f(x)=5x^2-3x+7, and f(g(x))=40-11x^2-8x^4. How do I find the sum of all possible coefficients of g(x)?
f(x)=5x^2-3x+7
f(g(x))=-8x^4-11x^2+40.
Should I let x^2 be a new variable? Where do I start?
1 Answer
- Anonymous2 years ago
f(x)=5x^2-3x+7
f(g(x))=-8x^4-11x^2+40.
g(x) is clearly some quadratic polynomial ax² + bx + c, with g(1) = a + b + c.
We have f(g(1)) = 40 – 11 – 8 = 31.
We want to solve f(x) = 21 to find g(1).
This gives 5x² - 3x + 7 = 21
5x² - 3x – 14 = 0
(5x + 7)(x - 2) = 0
X = -7/5, 2
These are the possible values of g(1) = a + b + c.