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

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0a n dalpha^2,beta is the roots of quadratic equation x^2-q x+8=0 , then the value of rifr/8 is the arithmetic mean of p a n d q , is

If alpha and beta are roots of the quadratic equation x ^(2) + 4x +3=0, then the equation whose roots are 2 alpha + beta and alpha + 2 beta 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

If alpha, beta are the roots of the quadratic equation x^2 + bx - c = 0 , the equation whose roots are b and c , is a. x^(2)+alpha x- beta=0 b. x^(2)-[(alpha +beta)+alpha beta]x-alpha beta( alpha+beta)=0 c. x^(2)+[(alpha + beta)+alpha beta]x+alpha beta(alpha + beta)=0 d. x^(2)+[(alpha +beta)+alpha beta)]x -alpha beta(alpha +beta)=0

If alphaandbeta be the roots of the quadratic equation x^(2)+px+q=0 , then find the quadratic equation whose roots are (alpha-beta)^(2)and(alpha+beta)^(2) .

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta + alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If alpha,beta are the roots of the equation ax^2 + bx +c=0 such that beta < alpha < 0 , then the quadratic equation whose roots are |alpha|,|beta| is given by

If alpha and beta are the roots of the quadratic equation x^(2) + px + q = 0 , then form the quadratic equation whose roots are alpha + (1)/(beta), beta + (1)/(alpha)

If the quadratic equation , 4^(sec^(2)alpha) x^(2) + 2x + (beta^(2)- beta + 1/2) = 0 have real roots, then find all the possible value of cos alpha + cos^(-1) beta .

If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is