Child Labor #5

Algebra Level 3

Given that x 3 − 8 x 2 + a x + b = 0 x^3 - 8x^2 + ax + b = 0 has integer roots. If b 2 + 22 b + 120 = 0 b^2 + 22b + 120 = 0 , find ( a + b ).


The answer is 7.

Rajen Kapur by Rajen Kapur , 72, India

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1 solution

Rajen Kapur
Jul 24, 2015

Using (b + 10)(b + 12) = 0, b = -10, or -12. Sum of the roots is 8 and the product is 10 ( i.e. 1, 2, and 5) or 12 (i.e. 1, 3, and 4). In any case 1 being the root, putting x = 1 in the given equation, 1 - 8 + a + b = 0, Hence (a + b ) = 7

1 Helpful 0 Interesting 0 Brilliant 0 Confused

n i c e ! ! ! nice!!!

Harshi Singh - 5 years, 10 months ago

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