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

Correct Answer: x2 - 8x + 12 = 0

Explanation:

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


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