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Question: If a + b = 3 and a<sup>3</sup> + b<sup>3</sup> = 7, then a and b are the roots of the equation...

If a + b = 3 and a3 + b3 = 7, then a and b are the roots of the equation

A

3x2 + 9x + 7 = 0

B

9x2 – 27x + 20 = 0

C

2x2 – 6x + 15 = 0

D

None of these

Answer

9x2 – 27x + 20 = 0

Explanation

Solution

Given a + b = 3, a3 + b3 = 7

(a + b)3 – 3ab (a + b) = 7

27 – 3ab (3) = 7

20 = 9 ab, ab = 209\frac{20}{9}

\Question which has roots a & b is

x2 – 3x + 209\frac{20}{9} = 0

9x2 – 27x + 20 = 0