If p and q are the roots of the equation x2 + px + q = 0, then

Q13 of 242 Page 9

If p and q are the roots of the equation x² + px + q = 0, then

Since p and q are roots of the equations then

Sum of the roots is p + q = = – (p) = – p

Here a = 1, b = p and c = q

Products of the root = p × q = = q

∴ p × q = q

p = 1

Putting value of ‘p’ in p + q = – p

1 + q = – 1

q = – 2

If the equation x² – bx + 1 = 0 does not possess real roots, then

If x = 1 is a common root of the equations ax² + ax + 3 = 0 and x² + x + b = 0, then ab =

If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax² + bx + 1 = 0 having real roots is

The number of quadratic equations having real roots and which do not change by squaring their roots is