Question

If a and b are roots of quadratic equation x2+ax+b=0 then find the values of a and b.

Answer 1

a=b=0 is the answer for the above quadratic equation

Answer 2

Answer:

The value of a and b are either a=0,b=0 or a=1, b=-2.

Step-by-step explanation:

If a quadratic equation is defined as $ax^2+bx+c=0$ and α and β are roots, then

$\alpha +\beta=\frac{-b}{a}$          ....(1)

$\alpha \times \beta=\frac{c}{a}$             .... (2)

The given equation is

$x^2+ax+b=0$

The a and b are roots of quadratic equation. Using equation (1) we get

$a+b=\frac{-a}{1}$

$a+b=-a$

$2a+b=0$                      ... (3)

Using equation (2), we get

$a\times b=\frac{b}{1}$

$ab-b=0$

$b(a-1)=0$

Equate each factor equal to 0.

$b=0$

$a=1$

If b=0, then by equation (3) a=0.

If a=1, then by equation (3) b=-2.

Therefore the value of a and b are either a=0,b=0 or a=1, b=-2.