6x^2-35x-5 ac method

Question

Please help me factor this out using the AC method.

a x c = -30 (factored out 2 x 3 x 5)

b=-35

b should be the sum of numbers whose product is -30.

I can't figure it out.

 

Thanks!

Answer 1

6x²-35x-5≡ax²+bx+c; a=6, ac=-30, b=-35, b²=1225, c=-5; 4ac=-120; 2a=12.

To solve the quadratic 6x²-35x-5=0, use the quadratic formula:

x=(-b±√(b²-4ac))/(2a) 

x=(35±√(1225+120))/12=(35±√1345)/12=5.97285 or -0.13952 (approx).

These are the zeroes of the quadratic x²-35x/6-⅚, so the original quadratic factorises:

6(x-5.97285)(x+0.13952)=6(x²-35x/6-⅚).

The product of the zeroes using these values is -0.83333 and c/6=-⅚=-0.83333 to the same accuracy.

The sum of the zeros is 5.97285-0.13952=5.83333 and -b/6=35/6=5⅚=5.83333 to the same accuracy.