# Further maths question help

Watch
Announcements
#1
one root of z^3 - 15z^ 2 + 76z - 140=0 is an integer. solve the equation
0
4 years ago
#2
Through trial and error, I got as factor of the equation. Now use the long division method so that you're left with an equation in the form of

Now you can't factorise the quadratic equation or use the quadratic formula because it doesn't satisfy so you'll need to complete the square to find the two other roots.

Spoiler:
Show

The roots I got:
, and

1
4 years ago
#3
There is something called the rational roots theorem which says that if any rational roots exist to a polynomial then they are of the form where is a factor of 140 (constant term) and is a factor of 1 (coefficient of leading term). So the only values you should need to try are 1, 2, 4, 5, 7, 10, 20, 28, 35, 70, 140. If any rational roots exist then they are one of these 22 values. Of course you find that 7 works quickly if you use a calculator.
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### Do you have the space and resources you need to succeed in home learning?

Yes I have everything I need (162)
59.78%
I don't have everything I need (109)
40.22%