If `alpha_1, alpha_2` be the roots of equation `x^2+px+q=0 and beta_1,beta` be those of equation `x^2+rx+s=0` and the system of equations `alpha_1y+alpha_2z=0 and beta_1 y+beta_2 z=0` has non trivial solution, show that `p^2/r^2=q/s`

If alpha_1, alpha_2 be the roots of the equation x^2-px+1=0 and beta_1,beta_2 be those of equatiion x^2-qx+1=0 and vecu=alpha_1hati+alpha_2hatj,and vecv=beta_1hati+beta_2hatj is parallel.

Let alpha_1,alpha_2 and beta_1, beta_2 be the roots of the equation ax^2+bx+c=0 and px^2+qx+r=0 respectively. If the system of equations alpha_1y+alpha_2z=0 and beta_1y+beta_2z=0 has a non trivial solution then prove that b^2/q^2=(ac)/(pr)

Let alpha_1,alpha_2 and beta_1, beta_2 be the roots of the equation ax^2+bx+c=0 and px^2+qx+r=0 respectively. If the system of equations alpha_1y+alpha_2z=0 and beta_1y+beta_2z=0 has a non trivial solution then prove that b^2/q^2=(ac)/(pr)

If alphaand beta the roots of the equation px^2+qx+1=0, find alpha^2beta^2.

If alpha_1,alpha_2 are the roots of equation x ^2-p x+1=0a n dbeta_1,beta_2 are those of equation x^2-q x+1=0 and vector alpha_1 hat i+beta_1 hat j is parallel to alpha_2 hat i+beta_2 hat j , then p= a. +-q b. p=+-2q c. p=2q d. none of these

If alpha and beta are the roots of the equation 2x^(2)+3x+2=0 , find the equation whose roots are alpha+1 and beta+1 .

Let alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

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

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

If alpha, beta are the roots of the equations x^2+px+q=0 then one of the roots of the equation qx^2-(p^2-2q)x+q=0 is (A) 0 (B) 1 (C) alpha/beta (D) alpha beta