If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0 then, ab =

Q18 of 242 Page 9

If x = 1 is a common root of ax² + ax + 2 = 0 and x² + x + b = 0 then, ab =

Since x = 1 is root of equation

Then it satisfy the equation

Putting x = 1 in first equation

a + a + 2 = 0

2a + 2 = 0

a = – 1

Putting x = 1 in equation second

1 + 1 + b = 0

2 + b = 0

b = – 2

ab = – 1 x – 2

ab = 2

If (a² + b²) x² + 2 (ac + bd) x + c² + d² = 0 has no real roots, then

If the sum of the roots of the equation x² – x = λ (2x – 1) is zero, then λ =

The value of c for which the equation ax² + 2bx + c = 0 has equal roots is

If x² + k (4x + k – 1) + 2 = 0 has equal roots, then k =