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प्रश्न
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
उत्तर
Compare quadratic equation x2 + 12x – k = 0
With ax2 + bx + c = 0
Then, a = 1, b = 12, c = –k
Let first root of given quadratic equation be α
According to question second root = 3α
We know that
Sum of roots = `-b/a`
α + 3α = `(-b)/a`
`\implies` 4α = `(-12)/1`
`\implies` α = –3
Product of roots = `c/a`
α × 3α = `(-k)/1`
3α2 = –k
Put the value of α
3 × (–3)2 = –k
k = –27
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