Question

If a, b be the roots $x^2+px-q$=0 and g,d be the roots of $x^2+px+r$=0 , q+r =1 then $\frac{(a-g)(a-d)}{(b-g)(b-d)}$ is ……

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A

1

Here, a+b= -p

g+d = -p

then a+b= g+d

now, (a-g)(a-d)= $a^2$– a(g+d)+gd

=$a^2–a(a+b)+r$ = -ab +r = -(-q)+r = q+r

By symmetry of the results (b-g)(b-d)= q+r

Hence , the ratio is 1