Quadratic discriminancy

Algebra Level 2

If the difference of the roots is 15 and the coeffecient of x^2 is 3,then find the discriminant?

2025 135 5 45

1 solution

Sujoy Roy
Dec 7, 2014

Let roots of the equation $ax^2+bx+c=0$ (hare $a=3$ ) are $\alpha$ and $\beta$ .

Now, $(\alpha-\beta)^2 = (\alpha+\beta)^2-4\alpha \beta$

or, $15^2=\frac{b^2}{a^2}-4\frac{c}{a}$

or, $\frac{b^2-4ac}{9}=225$

or, discriminant $(D)=b^2-4ac=225*9=\boxed{2025}$