The values of `alpha in R` for which the quadratic equation `3x^2+2(alpha^2+1)x+(alpha^2-3alpha+2)=0` possesses real roots of opposite sign are

The values of alpha in R for which the quadratic equation 3x^(2)+2(alpha^(2)+1)x+(alpha^(2)-3 alpha+2)=0 possesses real roots of opposite sign are

The real values of 'a' for which the quadratic equation 2x^2 - (a^3 + 8a - 1) x + a^2 - 4a = 0 possess roots of opposite sign is given by:

The real values of 'a' for which the quadratic equation 2x^(2)-(a^(3)+8a-1)x+a^(2)-4a=0 possesses roots of opposite sign is given by

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots

The value of alpha for which the equation (alpha+5)x^(2)-(2 alpha+1)x+(alpha-1)=0 has roots equal in magnitude but opposite in sign,is

IF alpha be a root of the quadratic equation 4x^2+2x-1=0 , Let prove that 4alpha^3-3alpha is the other root.