Question

Consider quadratic equations `x^(2)-ax+b=0`……….`(i)` and `x^(2)+px+q=0`……….`(ii)`
If for the equations `(i)` and `(ii)` , one root is common and the equation `(ii)` have equal roots, then `b+q` is equal to
A. `-ap`
B. `ap`
C. `(1)/(2)ap`
D. `2ap`

Answer 1

Correct Answer - C
`(c )` Let `alpha`, `beta` be the roots of `(i)` and `alpha`, `alpha` those of `(ii)`
`:.alpha+beta=a`, `alphabetb`, `2alpha=p`, `alpha^(2)=q`
`:. B+q=alpha(beta+alpha)=(1)/(2)p.a`