Question

solve the polynomial equation:
15x^3-119x^2-10x+16=0

Answer 1

tough question, I'd graph it using some software or a calculator, to find the x-intercepts because just doing a quick check there is a root between 0 and 1, closer to 0

Answer 2

x=8,x=-2/5,x=1/3

Answer 3

so how did you do it @pengembara_bumi1

Answer 4

First thing you can do without a calculator is find all possible roots of the equation, which uses the leading coefficient (15) and the constant (16). Now we find all the factors of these:
15 has 1,3,5,15
16 has 1,2,4,8,16

Now place every leading coefficient factor over every constant factor and you have all of your possible choices. This one is quite a pain in the neck without a calculator because the only way to find it is to go through short division of every factor possible into the coefficients.

Answer 5

just using calculator.. haha

Answer 6

(x-8)(x+2/5)(x-1/3)

Aren't the three constant terms supposed to multiply to give 16 though?

Answer 7

well remember that the coefficient of the leading term is 15 ... you cubic has a coefficient of the leading term being 1

Answer 8

15 has 1,3,5,15
16 has 1,2,4,8,16

Looking at this, you have: ±1, 1/3, 1/5, 1/15, 2, 2/3, 2/5, 2/15, 4, 4/3, 4/5, 4/15, 8, 8/3, 8/5, 8/15, 16, 16/3, 16/5, and 16/15 as possible values.

Answer 9

so why not just graph it rather than substituting a silly number of possible values into an equation.

Answer 10

I was always told to not use a calculator for some like these, including on tests that had upwards of 20 values to plug in without a calculator.

Answer 11

lol....my question to your teacher would be.... where is the higher learning in doing that

Answer 12

its interesting that you can use the rational root theorem but forgot about the actual equation... leading coefficient of 15.. but good luck with your maths