Question

if alpha and beta are the roots of the equation x2+ax-b+0, find alpha and beta?

Answer 1

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.