Two number whose sum is 8 and difference is 4, are the

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Two number whose sum is 8 and difference is 4, are the roots of the equation

1. x² + 8x + 12 = 0
2. x² + 8x - 12 = 0+
3. x² - 8x - 12 = 0
4. x² - 8x + 12 = 0
5. None of the above

Correct Option: D

Let the roots be α and β .
Then, α + β = 8 ......(i)
α - β = 4 ..(ii)
On solving Eqs. (i) and (ii), we get
α = 6, β = 2
∴ Required equation is
x² - (α + β) x + (α β) = 0
⇒ x² - (6 + 2)x + 6 x 2 = 0
⇒ x² - 8x + 12 = 0