Quadratic warm-up

Algebra Level 2

The equation y = x 2 + x y = x^2 + x has two distinct roots α \alpha and β \beta . Find α + β \alpha + \beta .


The answer is -1.

Viki Zeta by Viki Zeta , 19, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Viki Zeta
Jun 30, 2016

METHOD 1

y = x 2 + x The root of an equation is given by y = 0 = > y = 0 = > x 2 + x = 0 = > x ( x + 1 ) = 0 = > x = 0 , x = − 1 = > α = 0 , β = − 1 Therefore, α + β = 0 + ( − 1 ) = − 1 y = x^2+x\\ \text{The root of an equation is given by y = 0}\\ => y = 0\\ => x^2+x = 0\\ => x(x+1) = 0\\ => x = 0, x = -1\\ => \alpha = 0, \beta = -1\\ \text{Therefore, }\alpha + \beta = 0 + (-1) = -1

METHOD 2

y = x 2 + x Using the sum of zeros formula of quadratic equation, α + β = − b a Here a = 1, b = 1, c = 0 , = > α + β = − b a = − 1 1 = − 1 y = x^2+x\\ \text{Using the sum of zeros formula of quadratic equation, } \alpha + \beta = \frac{-b}{a} \\ \text{Here a = 1, b = 1, c = 0 }, => \alpha + \beta = \frac{-b}{a} = \frac{-1}{1} = -1

8 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...