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Consider quadratic equations x^(2)-ax+b=...

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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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