``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``

Find the value of alpha for which the equation (alpha-12)x^(2)+2(alpha-12)x+2=0 has equal roots.

The set of values of alpha for which the quadratic equation (alpha + 2) x^(2) - 2 alpha x - alpha = 0 has two roots on the number line symmetrically placed about the point 1 is

Find the value of alpha for which roots of equations are equal 4x ^(2) - 20 x + alpha = 0

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 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

If the roots of the equation 1/(x+p) + 1/(x+q) = 1/r are equal in magnitude but opposite in sign and its product is alpha

Let 4x^(2)-4(alpha-2)x + alpha-2=0(alpha in R) be a quadratic equation. Find the values of alpha for which Both the roots are equal in magnitude but opposite in sign

If both roots of quadratic equation (alpha+1)x^(2)-21-(1+3 alpha)x+1+8 alpha=0 are real and distinct then alpha be

If the roots alpha and beta (alpha+beta ne 0) of the quadratic equation ax^(2)+bx+c=0 are real and of opposite sign. Then show that roots of the equation alpha (x-beta)^(2)+beta(x-alpha)^(2)=0 are also real and of opposite sign.