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Find the roots of 6x^4 + 49x^3 + 128x^2 + 132x + 45.

 Jun 11, 2020
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If you can't do this by graphing, it's a painful process ...

 

If there are any rational solutions, the numerator is a divisor of 45:

     1, -1, 3, -3, 5. -5. 9. -9. 15. -15. 45. -45

and the denominator is a divisor of 6:

     1, -1, 2, -2, 3, -3, 6, -6

 

If you try enough of these, you'll find that both  -5/3  and  -3/2  are solutions.

 

This means that  3x + 5  and  2x + 3  are factors.

 

If you divide  6x4 + 49x3  128x2 + 132x + 45  by  (3x + 5)(2x + 4) 

you'll get the quotient  x2 + 5x + 3.

 

Then, apply the quadratic formula to  x2 + 5x + 3  to get the final two solutions.

 Jun 11, 2020

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