Write the value of λ for which x2 + 4x + λ, is a perfect square.

For being the perfect square, the roots are equalSo, d = b2 – 4ac = 0Here a = 1, b = 4 and c = λ⇒ d = 16 – 4 λ = 0⇒ λ = 4

Q8 of 242 Page 9

Write the value of λ for which x² + 4x + λ, is a perfect square.

For being the perfect square, the roots are equal

So, d = b² – 4ac = 0

Here a = 1, b = 4 and c = λ

⇒ d = 16 – 4 λ = 0

⇒ λ = 4

Write the set of values of 'a' for which the equation x² + ax – 1 = 0 has real roots.

Is there any real value of 'a' for which the equation

x² + 2x + (a² + 1) = 0 has real roots?

Write the condition to be satisfied for which equations ax² + 2bx + c = 0 and have equal roots.

Write the set of values of k for which the quadratic equation has 2x² + kx + 8 = 0 has real roots.