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.
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,
[tex]\frac{-b\pm\sqrt{(b^2-4ac}}{4a}[/tex]
Putting the values:
[tex]\frac{8\pm\sqrt{(64 - 4\times 2\times -24 }}{4\times2}[/tex]
[tex]\frac{8\pm\sqrt{280 }}{8}[/tex]
⇒8 ± √5
