Question

If alpha and beta are the zeroes of the polynomial f of x is equal to ax^2+bx+c, where a,b,c are non negative, then find the value of |alpha - beta |​

Answer 1

✪AnSwEr

• Taking Alpha=A and Beta =B

${\tt{\red{\underline{\large{Given}}}}}$

• A and B are the zeroes of polynomial
• f(X)=ax²+bx+c
• where a,b and c is non negative no

${\sf{\green{\underline{\large{To\:find}}}}}$

• |A-B|

${\sf{\pink{\underline{\Large{Explanation}}}}}$

☞

Here we know that

A+B = -b/a

and

• ☞AB=c/a

Now

(A-B)²=(A+B)²-4AB

=>(A-B)²=(-b/a)²-4(c/a)

=>(A-B)²=b²/a² -4c/a

=>(A-B)²=(b²-4ac)/a²

=>(A-B)=√(b²-4ac)/a²

=>(A-B)=√(b²-4ac)/a

Now |A-B|

|A-B|=|√(b²-4ac)/a|