Question

Given a quadratic equation, ax2+bx+c=0 if the ratio of the sum of the roots and the product of roots is 2:7, what can be possible values of b and c?

Answer 1

Answer:

Answer is above Stars

Step-by-step explanation:

Given a quadratic equation, $ax^2+bx+c=0$.

The sum of the roots and the product of roots is 2:7.

Two roots are α, β.

Then $ax^2+bx+c=0$ can be written as

• $a(x-\alpha )(x-\beta )=0$. → 1

From 1, $\alpha +\beta$, $\alpha \beta$ can be gotten without solving equation.

$a\{x^2-(\alpha +\beta )x+\alpha \beta \}=ax^2+bx+c$

It is an identity.

∴ $\alpha +\beta =-\frac{b}{a}$, $\alpha \beta =\frac{c}{a}$

$-\frac{b}{a} :\frac{c}{a}=2:7$

∴All Solutions that satisfies $-b:c=2:7$

∴$(b,c)=(-2,7),(2,-7),(-4,14),(-4,14),...$