Question

if roots of the equation ax^2+bx+c=0 are a-b and b-c then value of (a-b)(b-c)/c-a value will be
a.ab/c
b.c/b​

Answer 1

Answer:

b) c/b

Step-by-step explanation:

Given , the quadratic equation is

$a {x}^{2} + bx + c = 0$

Let us consider the roots of the quadratic equation be

$\alpha = a - b$

and

$\beta = b - c$

We know that ,

$sum \: of \: the \: roots \: = \frac{coefficient \: of \: x}{coefficient \: of {x}^{2} }$

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

And agan

$product \: of \: roots \: = \frac{constant \: term}{coefficient \: of \: {x}^{2} }$

$\implies \alpha. \beta = \frac{c}{a} \\ \implies(a - b)(b - c) = \frac{c}{a}$

Now we are given to find the value of

$\frac{(a - b)(b - c)}{c - a}$

Putting the values of (a - b)(b - c) and (c - a) we have

$\frac{(a - b)(b - c)}{(c - a)} \\ = \frac{\frac{c}{a} }{ \frac{b}{a} } \\ = \frac{c}{b}$

Answer 2

Answer:

answer is b

easy peasy

loll