Question
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 = 920
\Question which has roots a & b is
x2 – 3x + 920 = 0
9x2 – 27x + 20 = 0