Question

Form the quadratic equation whose roots are
3 and 10

Answer 1

Let $\alpha$ = 3 and $\beta$ = 10
Then, $\mathrm{\alpha }+\mathrm{\beta }$ = 3 + 10 = 13 and $\mathrm{\alpha \beta }=3\times 10$ = 30
We know that if $\alpha$ and $\mathrm{\beta }$ are the roots of a quadratic equation, the equation is
x² – ($\mathrm{\alpha }+\mathrm{\beta }$)x + $\mathrm{\alpha \beta }$ = 0
On substituting $\mathrm{\alpha }+\mathrm{\beta }$ = 13 and $\mathrm{\alpha \beta }$=30 , we get:
x² – 13x + 30 = 0