Question

if the roots of ax^2+bx+c=0 are -1,-1 then a:b:c? answer =1 :3 : 2
explanation please1!!!

Answer 1

Question -

If the roots of ax² + bx + c = 0 are -1, -1 then a:b:c ?

Answer -

1:2:1

Solution -

let $\alpha = -1$ and $\beta = -1$ be the zeros of the equation ax² + bx + c = 0.

Thus,

$\quad \ \alpha + \beta = - \dfrac{b}{a}$

$\Rightarrow -1 -1 = - \dfrac{b}{a}$

$\Rightarrow 2 = \dfrac{b}{a}$

$\Rightarrow b = 2a$

And,

$\quad \ \alpha \times \beta = \dfrac{c}{a}$

$\Rightarrow (-1) \times (-1) = \dfrac{c}{a}$

$\Rightarrow 1 = \dfrac{c}{a}$

$\Rightarrow c = a$

Hence

$\quad \: a : b : c$

$= a : 2a : a$

$= \cancel{a} : 2 \cancel{a} : \cancel{a}$

$= 1 : 2 : 1$