Question

If one root of quadratic equation x2 +12x-k=0 is trice the other find the value of k ]

Answer 1

p(x) = x²+ 12x - k = 0
Let α=3β
then, α+β = -b/a
3β+β = -12
β = -3
Now we have found one root we'll substitute in p(x) to find the value of k.
p(x) = x²+ 12x - k = 0
⇒ (-3)² - 12(-3) -k = 0
⇒ 9 - 36 - k = 0
⇒ -27 - k = 0
∴ k = -27
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