Review question

# Can we find both roots if one is double the other? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6638

## Suggestion

Given that one of the values of $x$ satisfying the quadratic equation $x^2-(2a+1)x+(a^2+2)=0$ is twice the other, find $a$.

If we know the values of $x$ that satisfy a quadratic equation, how can we use this to write the equation down?

Could we now compare our equation with the one given?

The green curve here is $y=x^2-(2a+1)x+(a^2+2)$.

The blue line segment $OP$ represents the smaller root, and the length $OP'$ is double $OP$.