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 . 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

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 . 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

Find the values of k for which the equation x^(2)-4x+k=0 has distinct real roots.

Is there any real value of 'a' for which the equation x^(2)+2x+(a^(2)+1)=0 has real roots?

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

The number of real roots of the polynomial equation x^(4)-x^(2)+2x-1=0 is

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