# Question #82350

Jun 19, 2015

Neither of you is correct. The real zeros of this polynomial are 1 and 4.

#### Explanation:

The easiest way to see this is by using the quadratic formula.
If you have a polynomial in the form of $a x + b y + c$, then you can find both the real zeros like this:
1) $\frac{- b - \sqrt{{b}^{2} - 4 a c}}{2 a}$

2) $\frac{- b + \sqrt{{b}^{2} - 4 a c}}{2 a}$

In this case $a = - 1$, $b = 5$ and $c = - 4$.
Plugging this in the formula you get:

1) $\frac{- 5 - \sqrt{{5}^{2} - 4 \cdot \left(- 1\right) \cdot \left(- 4\right)}}{2 \left(- 1\right)} = 4$

2) $\frac{- 5 + \sqrt{{5}^{2} - 4 \cdot \left(- 1\right) \cdot \left(- 4\right)}}{2 \left(- 1\right)} = 1$

So remember this formula:

$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Jun 19, 2015

There is no answer, where there is no question.

#### Explanation:

$- {x}^{2} + 5 x - 4$ is an expression, it is not a question.

If the question is: "Evaluate $- {x}^{2} + 5 x - 4$ when $x = 1$, then your teacher is correct.

If the question is: "For what value of $x$ does the expression evaluate to $- 868$, then you are correct

If the question is something else, (Like where is the vertex of $y = - {x}^{2} + 5 x - 4$) then it is possible that neither of you is correct.