Question

If a and b are roots of the equations x 2 +ax+b=0 then a+b = (a) -1 (b) 1 (c) 2 (d) -2

Answer 1

(a) -1

EXPLAINATION

GIVEN

• Quadratic Equation x² + ax + b = 0
• 'a' and 'b' are roots of the equation.

CALCULATION

Using relation between roots and co-efficient

Sum of roots = $-\frac{Co-efficient\:\: of \:\: x} {Co-efficient\:\: of\:\: x²}$

$⇒ a +b = - \frac{a}{1} = -a$

$⇒ 2a +b = 0-----(1)$

Product of roots = $\frac{Constant\:\: term} {Co-efficient\:\: of\:\: x²}$

$⇒ a\times b = \frac{b}{1} = b$

$⇒ a\times b- b = 0$

$b(a - 1) = 0$

$b = 0 \: or \: a = 1$

When b = 0, from (1)

$2a + 0 = 0$

$a = 0$

$so \: a + b = 0$

When a = 1, from (1)

$2 \times 1 + b = 0$

$b = - 2$

$so \: a + b = 1 - 2 = - 1$