Question
If a + b +c = 0, then the equation 3ax2+2bx+c=0 has, in the interval (0, 1)
Answer: Option A
:
A
Let f(x)=anXn+an−1Xn−1+...+a2x2+a1x+a0
Which is a polynomial function in x of degree n. Hence f(x) is continuos and differentiable for all x.
Let ∞<β . We given, f (∞)=0=f(β).
By Rolle's theorem, f' (c) = 0 for some value c,
∞<c<β.
Hence the equation
F′(x)=nanxn−1+(n−1)an−1xn−2+...+a1=0
has atleast one root between ∞andβ.
Hence (c) is the correct answer.
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:
A
Let f(x)=anXn+an−1Xn−1+...+a2x2+a1x+a0
Which is a polynomial function in x of degree n. Hence f(x) is continuos and differentiable for all x.
Let ∞<β . We given, f (∞)=0=f(β).
By Rolle's theorem, f' (c) = 0 for some value c,
∞<c<β.
Hence the equation
F′(x)=nanxn−1+(n−1)an−1xn−2+...+a1=0
has atleast one root between ∞andβ.
Hence (c) is the correct answer.
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