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If a and b are roots of x^2 + px + q = 0 and c and d are the roots of x^2 + px - r = 0 then (a-c)(a-d) is equal to _______? (answer in terms of p and q and r)

If a and b are roots of x^2 + px + q = 0 and c and d are the roots of x^2 + px - r = 0 then (a-c)(a-d) is equal to _______?


(answer in terms of p and q and r)

Grade:11

1 Answers

Aman Bansal
592 Points
9 years ago

Dear Shaurya,

x 2 ? p x ? q ? 0
? ?? ? ?p ..........................(1)
?? ? ?q ..........................(2)
x 2 ? p x ? r ? 0
? ?? ? p ..........................(3)
?? ? r ..........................(4)
Now
?? ?? ??? ?? ?
= ? 2 ? ?? ?? ?? ???
= ? 2 ? p? ? r using (3) & (4)
= q + r ? (? is root of x2 + px - q = 0
? ? 2 ? p? ? q ? 0
? ? 2 ? p? ? q )

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