Grade 11Algebra

if the equation [b-c]x2+[c-a]x+a-c=0,,,,has equal roots then prove 2b=a+c

aditya kulkarni

15 Years agoGrade 11

2 Answers

Vinay Goyal IITB

15 Years ago

Dear aditya,

I think there is some problem in question. As you have told equation has equal roots then its descriminant will be 0

so B²=4AC

[c-a]²=4[b-c][a-c] on solving this you get 4b=3c+a

jagdish singh singh

15 Years ago

$Here equation is $(b-c)^2+(c-a)x+(a-b)=0$\\\\ So Clearly one Root is $x=1$\\\\ Let This Root be $\alpha=1$ and other Root be $\beta$\\\\ so $\alpha.\beta=\frac{a-b}{b-c}\Leftrightarrow \beta=\frac{a-b}{b-c}$\\\\ so Here It is Given $\alpha=\beta\Leftrightarrow 1=\frac{a-b}{b-c}$\\\\ so $a-b=b-c\Leftrightarrow \boxed{\boxed{2b=a+c}}$