If ax²+bx+c=0 and bx²+cx+a=0 have a common root and a≠0 then a³+b³+c³/abc=

If α, β are different values of θ satisfying the equations 5 cos θ+12 sin θ=11 then the value of sin (α+β)=

The quadratic equation x² + ax + bc = 0, x² + bx + ca = 0 have a common root, then the quadratic equations whose roots are the remaining roots in the given equations is (where, a ≠ b)

If α,β are the roots of ax²+bx+c=0 then (α/β – β/α)²=

α and β are the roots of the equation x²+px+p³=0,(p≠0).If the points (α,β) lies on the curve x=y²,then the roots of the given equation are

If the roots of x²+bx+c=0 are two consecutive integers then b²-4c=

A number consists of two digits whose product is 30.If the digits are interchanged the resulting numbers will exceed the previously by 9.The number is

If the roots of x²-2(5+2k)x+3(7+10k)=0 are equal then k=

The quadratic equations x² – 6xa = 0 and x² – cx + 6 = 0 and have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

3x-5x²+12 has maximum at x=