Question

which shows the correct substitution of the values a, b, and c from the equation -2=-x+x^2-4 into the quadratic formula?

Quadratic formula: x= -b+_ square root b^2-4ac / 2a

Answer 1

Given the equation:

(1) $-2=-x+ x^{2}-4$

We need to find a, b and c. So, we know that a quadratic equation is given by:

(2) $ax^{2}+bx+c=0$

Then, we need to order the equation (1) and to adjust it to the equation (2), so:

$x^{2}-x-2=0$

So, if we compare these two equations, the conclusion is:

$a=1$
$b=-1$
$c=-2$

(3) $x= \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

Substituiting a, b and c into (3):

$x= \frac{-(-1)\pm \sqrt{(-1)^{2}-4(1)(-2)}}{2(1)}$

Finally, the results are two values:

$x_{1}=2$
$x_{2}=-1$

Answer 2

The correct substitution of a, b and c in the quadratic formula is as follows:

$\frac{-(-1) +\sqrt{(-1)^{2}-4(1)(-2) } }{2(1)}$

Quadratic equation

The quadratic equation follows the pattern,

• ax² + bx + c

The given equation have to b arrange in the format above to know the value of a, b and c.

Therefore,

-2 = -x + x²- 4

x² - x - 4 +2 = 0

x² - x - 2

Therefore,

a = 1

b = -1

c = -2

Using the quadratic formula

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

The correct substitution is as follows

$\frac{-(-1) +\sqrt{(-1)^{2}-4(1)(-2) } }{2(1)}$

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