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Question
If -1 and 3 are the roots of x2+px+q=0
then find the values of p and q
Solution
Since -1 is a root of x2 + px + q = 0, we have
(-1)2 + p(-1) + q = 0
⇒ 1 - p + q = 0
⇒ -p + q = -1.......(i)
Also, 3 is a root of x2 + px + q = 0
⇒ (3)2 + p(3) + q = 0
⇒ 9 + 3p + q = 0
⇒ 3p + q = -9.......(ii)
Subtracting equation (ii) from (i), we get
-4p = 8
⇒ p = -2
⇒ -(-2) + q = -1 ...........[From (i)]
⇒ 2 + q = -1
⇒ q = -3
Hence, p = -2 and q = -3
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