Question

can you help me find the roots of the polynominal of 5x^2 -x....

I also need help in finding the factorization of x^2 - 15x + 56

help in solving the the equation x^2 + 30x = 1000....thank you

Answer 1

1. 5x^2-x
You can find the roots to an equation (which always has an equal sign) or you can (or cannot) factorize a polynomial.
Since the expression is a polynomial, you can certainly factorize it. Look for common symbols as a first step.

2. x^2-15x+56
These are relative easy if you know that
(x-a)(x-b) = x^2 - (a+b)x + ab
which reduces your problem to looking for the values of a and b such that
ab=56, and a+b=15.
Give it a go, I know you can do it.

3. x^2+30=1000
The solution of the equation can be reduced to a factorization problem.
The equation can also be written as
x^2 + 30 -1000 =0

Since (x+a)(x-b)=x^2+(a-b)-ab (if a>b)
we look for values of a and b such that
ab=1000
a-b=30
Since the number of factors of 1000 are limited, you should have no problem finding a and b.
since (x+a)(x-b)=0 implies
x+a=0, OR x-b=0,
you will be able to solve for the two possible values of x once you know a and b.