Sum of the roots of a quadratic equation is double their product. Find k if equation is

x² – 4kx + k + 3 = 0

Determine the nature of roots of the following quadratic equation.

m² + 2m + 9 = 0

Form the quadratic equation from the roots given below.

(1) 0 and 4

(2) 3 and -10

(3)

(4)

α, β are roots of y² – 2y – 7 = 0 find,

(1) α² + β²

(2) α³ + β³

The roots of each of the following quadratic equation are real and equal, find k.

3y² + ky + 12 = 0