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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 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)-14x^(2)+24x-k=90 has four unequal real roots is

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

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 . Q.The exhaustive range of values of k for which the equation x^(4)-14x^(2)+24x-k=0 has four unequal real roots is

If f(x) is a polynomial of degree 5 with real coefficients such that f(|x|)=0 has 8 real roots, then f(x)=0 has

If f(x)=x^(3)-3x+1, then the number of distinct real roots of the equation f(f(x))=0 is

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Number of real roots of equation f(x)=0 is (A) 0 (B) 1 (C) 2 (D) none of these

The equation whose roots are reciprocals of the roots of the equation f(x)=0 is