Number of integral value of `beta` for which equation `x^(4)+4x^(3)+10x^(2)+12x+7-beta=0` has four distinct real roots is

The number of positive integral values of m , m le 16 for which the equation (x^(2) +x+1) ^(2) - (m-3)(x^(2) +x+1) +m=0, has 4 distinct real root is:

Find the integral values of a for which the equation x^(4)-(a^(2)-5a+6)x^(2)-(a^(2)-3a+2)=0 has only real roots

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

The numberof real values of x that satisfies the equation x^(4)+4x^(3)+12x^(2)+7x-3=0 is

The real values of lambda for which the equation,4x^(3)+3x^(2)-6x+lambda=0 has two distinct real roots in [0,1] lie in the interval (A)(0,oo)(B)(3,oo)(C)(-5,(7)/(4))(D)[0,(7)/(4))

Number of integral values of 'a' for which the equation cos2x+3sin x+4sin^(2)x=a-3 has a real root is/are

Find the set of values of lambda for which the equation |x^(2)-4|x|-12]=lambda has 6 distinct real roots.

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