`x^2+3x-4`, find Rational Zeros Theorem to find all possible rational roots

Solution:
The Given Polynomial `=x^2+3x-4`

`=x^2+3x-4`



Step-1: Find the constant and its factors (both positive and negative)
The constant term is 4
and its factor are, `p=+-1,+-2,+-4`

Step-2: Find the leading coefficient and its factors (both positive and negative)
The leading coefficient is 1
and its factor are, `q = +-1`

Step-3: Find all possible values of `+-p/q`

When `q=+-1` then `p/q=+-1/1,+-2/1,+-4/1`

Step-4: Simplify and remove any duplicates

The possible rational roots are `+-1,+-2,+-4`

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Step-5: Now substitute these possible roots in f(x) and if `f(x)=0` then it is the actual rational roots (actual rational zeros)

`f(x)=x^2+3x-4`

1.  `f(1)=(1)^2+3(1)-4=0`

Hence, `1` is a root.

2.  `f(-1)=(-1)^2+3(-1)-4=-6`

3.  `f(2)=(2)^2+3(2)-4=6`

4.  `f(-2)=(-2)^2+3(-2)-4=-6`

5.  `f(4)=(4)^2+3(4)-4=24`

6.  `f(-4)=(-4)^2+3(-4)-4=0`

Hence, `-4` is a root.

The actual rational roots are `1,-4`