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, beta, gamma are the roots of 9x^3 - 7x + 6 = 0 , then alpha beta gamma is …………

If alpha,beta are the roots of x^2+p x+q=0a n dgamma,delta are the roots of x^2+p x+r=0, then ((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))= a. 1 b. q c. r d. q+r

If alpha and beta are the roots of x^(2) + x + 1 = 0, then alpha^(2020) + beta^(2020) is

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+qx+r , where a , b , c , q , r in R and a lt 0 . If alpha , beta are the roots of f(x)=0 and alpha+delta , beta+delta are the roots of g(x)=0 , then

If alpha,betaa n dgamma are roots of 2x^3+x^2-7=0 , then find the value of sum(alpha/beta+beta/alpha) .

If alpha,beta are the roots of x^2+p x+q=0a n dgamma,delta are the roots of x^2+r x+s=0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in terms of p ,q ,r ,a n dsdot Deduce the condition that the equation has a common root.

If alpha and beta are the roots of equation x^(2)-4x+1=0 , find (i) alpha^(2)+beta^(2) (ii) alpha^(3)+beta^(3)

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

If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots of x^2+q x+1=0 , then prove that q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta) .