If a,b are roots of quadratic equation x^2+px+q=0 and c,d are roots of x^2+px-r=0 , then (a-c)(a-d) is equal to (A)q+r (B)q-r (C)-(q+r) (D)-(p+q+r)

Question

Deepak Kumar Shringi · Answer

as a is root of equation (i) it will satisfy it so
a²+ap+q=0
a²+ap=-q....(A)
c+d=-p....(I)
cd=-r..(ii)
(a-c)(a-d)
=a²-(c+d)a+cd {now use (i) & (ii)}
=a²+ap-r {now use (A)}
=-q-r option C is correct

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If a,b are roots of quadratic equation x^2+px+q=0 and c,d are roots of x^2+px-r=0 , then (a-c)(a-d) is equal to (A)q+r (B)q-r (C)-(q+r) (D)-(p+q+r)

If a,b are roots of quadratic equation x^2+px+q=0 and c,d are roots of x^2+px-r=0 , then (a-c)(a-d) is equal to
(A)q+r
(B)q-r
(C)-(q+r)
(D)-(p+q+r)

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If a,b are roots of quadratic equation x^2+px+q=0 and c,d are roots of x^2+px-r=0 , then (a-c)(a-d) is equal to (A)q+r (B)q-r (C)-(q+r) (D)-(p+q+r)

If a,b are roots of quadratic equation x^2+px+q=0 and c,d are roots of x^2+px-r=0 , then (a-c)(a-d) is equal to(A)q+r(B)q-r(C)-(q+r)(D)-(p+q+r)

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If a,b are roots of quadratic equation x^2+px+q=0 and c,d are roots of x^2+px-r=0 , then (a-c)(a-d) is equal to
(A)q+r
(B)q-r
(C)-(q+r)
(D)-(p+q+r)