Question

What are the solutions to the quadratic equation 2x^2-8x-24=0

Answer 1

2x^2 - 8x - 24

First, we can factor a 2 out of this expression to simplify it.

2(x^2 - 4x - 12)

Now, we can try factoring this two ways: by using the quadratic formula, or by using the AC method.

We're gonna try using the AC method first.

List factors of -12.

1 * -12

-1 * 12

2 * -6

-2 * 6 (these digits satisfy the criteria.)

Split the middle term.

2(x^2 - 2x + 6x - 12)

Factor by grouping.

2(x(x - 2) + 6(x - 2)

Rearrange terms.

(2)(x + 6)(x - 2) is the fully factored form of the given polynomial.

Answer 2

Answer:

8 ± √5

Step-by-step explanation:

2x² - 8x - 24 = 0

Here Discriminant(D) = b² - 4ac > 0.

Here a is the coefficient of x²

b is the coefficient of x

c is the constant term

Thus, it has Real roots.

Now, using the Sridharayacharya Formula,

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

Putting the values:

$\frac{8\pm\sqrt{(64 - 4\times 2\times -24 }}{4\times2}$

$\frac{8\pm\sqrt{280 }}{8}$

⇒8 ± √5