Polynomials Question need help. (1 Viewer)

[Leffife]

Question: 4x³ + ax² + bx + 6 = 0 has roots 2,3 and α. Find the values of a, b and α.

My working out:

2x3xα = -6/4
6α = -6/4
α = -1/4

2 + 3 + a = -a/4
2 + 3 - 1/4 = -a/4
-a = 19
a = - 19

I'm not sure how to get b though. Thank you.

 

[zeebobDD]

product of the roots two at a time, so 6 + 3a + 2a = b/4 continue from there

 

[thorax94]

Question: 4x³ + ax² + bx + 6 = 0 has roots 2,3 and *. Find the values of a, b and *.

Sum of roots 2 at a time
ab+ b*+ a* = b/4
6 + 3*+ 2* = b/4
6-(3/4) - (1/2) = b/4
19/4 = b/4
19= b
b=19