If `3` and `-3` are the solutions of equation `ax^(2)+bx-9=0`, find the values of a and b.

If (2)/(3) and -(1)/(2) are solution of quadratic equation 6x^(2)+ax-b=0 , find the values of a and b.

If sqrt((2)/(3)) is a solution of equation 3x^(2)+mx+2=0 , find the value of m.

If sin theta, cos theta are the roots of the equation ax^(2)+bx+c=0 then find the value of ((a+c)^(2))/(b^(2)+c^(2))

If x=(2)/(3) is a solution of the quadratic equation 7x^(2)+mx-3=0 , find the value of m.

Suppose 1,2,3 are the roots of the equation x^4 + ax^2 + bx + c = 0 . Find the value of c.

If alpha, beta be the roots of quadratic equation ax^(2)+bx+c=0 , then find the value of (a alpha^(2)+c)/(a alpha+b)+(a beta^(2)+c)/(a beta+b) ?

If 1,2,3 are the roots of the equation x^(3) + ax^(2) + bx + c=0 , then

If the roots of the equation ax^(2)+bx+c=0 be in the ratio 3:4, show that 12b^(2)=49ac .

If sin theta and cos theta are the roots of the quadratic equation ax ^(2) +bx + c=0(a ne 0). Then find the value of (b ^(2) -a^(2))/(ac ).