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

kx (x-2) + 6 = 0

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

Product of Pragati’s age 2 years ago and 3 years hence is 84. Find her present age.

The sum of squares of two consecutive natural numbers is 244; find the numbers.