Quadratic EquationHard
Question
Let f(x) = a6x6 + a5x5 + a4x4 + ...... + a0 be a real polynomial such that a0 ∈ R+ and a0 + 
< 0.
The equation f(x) = 0
< 0.The equation f(x) = 0
Options
A.has a real root in (-1, 1)
B.has no real roots in (-1, 1)
C.has no real roots.
D.has all the roots equal.
Solution
f(x)dx = 2 
< 0⇒ There exists x ∈ (-1, 1) with f(x) < 0
Also f(0) = a0 > 0
∴ f(x) = 0 has a root in (-1, 1)
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