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

(1) 3y2 + ky + 12 = 0 Solution: (2) kx (x-2) + 6 = 0 Solution:

## a, b are roots of y2 – 2y – 7 = 0 find,

(1) α2 + β2 Solution: (2) α3 + β3 Solution:

## Sum of the roots of a quadratic equation is double their product. Find k if equation is x2 – 4kx + k + 3 = 0

## Form the quadratic equation from the roots given below.

(1) 0 and 4 Solution: (2) 3 and -10 Solution: (3) ½, – ½ Solution: (4) 2 – √5, 2 + √5 Solution:

## Determine the nature of roots of the following quadratic equations.

(1) x2 – 4x + 4 = 0 Solution: (2) 2y2 – 7y + 2 = 0 Solution: (3) m2 + 2m + 9 = 0 Solution:

## Find the value of discriminant.

(1) x2 + 7x – 1 = 0 Solution: (2) 2y2 – 5y + 10 = 0 Solution: (3) √2×2 + 4x + 2 √2 = 0 Solution:

## Fill in the gaps and complete.

Solution:Roots are distinct and real when b2 – 4ac = 5, not real when b2 – 4ac = -5. Solution:x2 + 7x + 5 = 0 Solution: