If the equations`x^2 - px + q = 0 and x^2 - ax +b=0` have a common root and the second equation has equal roots then

Options

A. `aq=2(b+p)`
B. `aq=(b+q)`
C. `ap=2(b+q)`
D. `ap=b+q`

Answer

C

Explanation

Given equations are `x^(2) - px + q = 0 " "` …(1)
and ` x^(2) - ax + b = 0 " "` …(2)
Roots of second equation is
` x= (apm sqrt(a^(2)-4b))/2`
Since, Roots of second equation are equal discriminant =0
` :. sqrt(a^(2) -4b) = 0 rArr a^(2) = 4b " "`...(3)
` :. x = a/2`
Since , Equation (1) and (2) have common roots.
` :. x= a/2 " is the root of equation (1) also "`
Thus, `x=a/2` satisfies (1)
` rArr (a/2)^(2) = p ( a/2) + q =0 `
` rArr a^(2)/4 = pa /2 - q rArr 2b = pa - 2q" "`(from (3)
`rArr ap = 2 ( b+q)`