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Question
If – 4 is a root of the equation x2 + px – 4 = 0 and if the equation x2 + px + q = 0 has equal roots, find the values of p and q.
Solution
f(x) = x2 + px – 4 = 0
If – 4 is a root, then
f(– 4) = (– 4)2 + P(– 4) – 4
= 16 – 4p – 4 = 0
12 – 4p = 0
– 4p = – 12
p = 3
x2 + 3x + q = 0 has equal roots,
∆ = b2 – 4ac = 0
32 – 4 × 1 × q = 0
9 – 4q = 0
– 4q = – 9
q = `9/4`
p = 3, q = `9/4`
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