Question

Form the quadratic equation if its roots are

$5and-7$

Answer 1

Let α = 5 and β = –7. Then, α + β = 5 + (–7) = –2 and $\alpha \times \beta =5\times \left(-7\right)=-35$

We know that if α and β are the roots of a quadratic equation, the equation is

$x^2-\left(\alpha +\beta \right)x+\alpha \beta =0$

On substituting α + β = –2 and αβ = –35, we get:

x² – (–2)x + (–35) = 0

$\Rightarrow$ x² + 2x – 35 =0