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 opposite in sign

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

Let 4x^2 - 4(alpha - 2)x + alpha - 2 = 0 (alpha in R) be a quadratic equation. Find the values of 'a' for which (i) Both roots are real and distinct. (ii) Both roots are equal. (iii) Both roots are imaginary (iv) Both roots are opposite in sign. (v) Both roots are equal in magnitude but opposite in sign

If alpha and beta are the roots of the quadratic equation x^(2) - 4x - 6 = 0 , find the values of alpha^(2) + beta^(2) .

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

If alpha,beta in R and the quadratic equations x^2+2x+7=0a n d4x^2+alphax+beta=0 have atleast one common roots, then the value of alpha+beta is

If alpha,beta are roots of x^2-3x+a=0 , a in R and alpha <1< beta then find the value of a.

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+1 , then the value of (1)/(alpha beta)+(alpha+beta) is

If alpha and beta are the roots of the equation x^2+sqrt(alpha)x+beta=0 then the values of alpha and beta are -

If alpha and beta are the roots of a quadratic equation such that alpha+beta=2, alpha^4+beta^4=272 , then the quadratic equation is

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot