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Let f(x)=0 be a polynomial equation with...

Let `f(x)=0` be a polynomial equation with real coefficients. Then between any two distinct real roots of `f(x)=0`, there exists at least one real root of the equation `f'(x)=0`. This result is a consequence of the celebrated Rolle's theorem applied to polynomials. Much information can be extracted about the roots of `f(x)=0` from the roots of `f'(x)=0`.
If the roots of `x^(3)-12x+k=0` lie in `(-4, -3),(0, 1)` and (2, 3)`, then the range of values of k is

A

`4 lt k lt 11`

B

`9 lt k lt 11`

C

`8 lt k lt 13`

D

`4 lt k lt 13`

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The correct Answer is:
B
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Let f(x)=0 be a polynomial equation with real coefficients. Then between any two distinct real roots of f(x)=0 , there exists at least one real root of the equation f'(x)=0 . This result is a consequence of the celebrated Rolle's theorem applied to polynomials. Much information can be extracted about the roots of f(x)=0 from the roots of f'(x)=0 . If the three roots of x^(3)-12x+k=0 lie in intervals (-4,-3), (0,1) and (2,3) ,then the exhaustive range of values of k is

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Let f(x)=0 be a polynomial equation with real coefficients. Then between any two distinct real roots of f(x)=0 , there exists at least one real root of the equation f'(x)=0 . This result is a consequence of the celebrated Rolle's theorem applied to polynomials. Much information can be extracted about the roots of f(x)=0 from the roots of f'(x)=0 . The range of values of k for which the equation x^(4)+4x^(3)-8x^(2)+k=0 has four real and unequal roots is

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FIITJEE-TIPS-PARAGRAPH BASED (MULTIPLE CHOICE) (COMPREHENSION - I)
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