Find the values of `a` for which all the roots of the euation `x^4-4x^3-8x^2+a=0` are real.

Find the values of a for which all roots of the equation 3x^(4) + 4x^(3) – 12x^(2) + a = 0 are real and distinct.

Find the values of a for which the roots of the equation x^(2)+a^(2)=8x+6a are real.

Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=0 has all real solutions

Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=0 has two real solutions

Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=0 has no real solution

The least +ve integral value of 'a' for which the equation 3x^4 +4x^3-12x^2 +5a=0 has no real root is

Find how many roots of the equations x^(4)+2x^(2)-8x+3=0

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

Number of distinct real roots of equation 3x^4+4x^3-12x^2+4=0

Find the value of p for which the quadratic equation x(x-4)+p0 has real roots.