Question

Which equation could be solved using this application of the quadratic formula?
-2 + 22 – 4(1)(-4)
2(1)
I

Answer 1

Answer:

C. x^2 + 2x - 1 = 3

Step-by-step explanation:

The standard form of a quadratic equation is

ax^2 + bx + c = 0

We need to use the quadratic formula and the given expression to find the values of a, b, and c.

The quadratic formula is

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Where the formula has -b, the problem has -2, so b = 2.

Now we have

ax^2 + 2x + c = 0

In the denominator, where the formula has 2a, the problem has 2(1), so a = 1.

Now we have

x^2 + 2x + c = 0

Inside the root, the quadratic formula has -4ac. the problem shows -4(1)(-4). Since we already know that a = 1, then c = -4.

Now we have

x^2 + 2x - 4 = 0

Let's look at choice A.

x^2 + 1 = 2x - 3

Subtract 2x from both sides. Add 3 to both sides.

x^2 - 2x + 4 = 0   This is not it!

Let's look at choice B.

x^2 - 2x - 1 = 3

Subtract 3 from both sides.

x^2 - 2x - 4 = 0     This is not it!

Let's look at choice C.

x^2 + 2x - 1 = 3

Subtract 3 from both sides.

x^2 + 2x - 4 = 0     This is it!

Answer: C. x^2 + 2x - 1 = 3

Answer 2

$x^{2} +2x -1=3$ equation could be solved using this application of quadratic formula.

Option D is correct.

What is quadratic equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is  $ax^{2} +bx +c =0$, where a and b are the coefficients, x is the variable, and c is the constant term.

Quadratic formula

The quadratic formula is used to find the roots of a quadratic equation.

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

According to the question

$x=\frac{-2 \pm \sqrt{2^{2} -4(1)(-4)} }{2.1}$

We all know the quadratic formula for finding the factors of a quadratic equation

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

By comparing two formulas we get a = 1, b = 2, c = -4

Standard form of quadratic equation is $ax^{2} +bx +c =0$

Substitute a = 1, b = 2, c = -4 in the standard form of quadratic equation

⇒ $x^{2} +2x-4=0$

We can write it as

⇒ $x^{2} +2x -1=3$

$x^{2} +2x -1=3$ equation could be solved using this application of quadratic formula.

Option D is correct.

Find out more information about quadratic formula here

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