If the two equations x²-cx+d=0 and x²-ax+b=0 have a common root and the second equation has equal roots,then

If the system of equations x + y + z =6, x + 2y + 3z=10 has no solution then λ=

If b²-4ac>0,then the graph of y= ax²+bx+c

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