Question

Write the quadratic equation in factored form. Be sure to write the entire equation. x2 - 5x - 24 = 0

Answer 1

Answer:
`(x-8)(x+3)=0`

Explanation:

The standard quadratic equation is
`ax^2+bx+c=0`

Given quadratic equation:-
`x^2-5x-24=0`, here a=1, b= -5, c= -24

Now, factorize given functions, first find two numbers that multiply to give ac and add to give b

ac=1×-24= -24

After checking factors of -24 we found -8 and 3 which multiply to give -24 and add to give -5

Rewrite the equation by writing -5 as sum of -8 and 3, we get

`x^2+(-8+5)x-24=0\\\Rightarrow\ x^2-8x+3x-24=0\\\Rightarrow\ (x^2-8x)+(3x-24)=0\\\Rightarrow\ x(x-8)+3(x-8)=0\\\\[\text{Take (x-8) as common outside}]\\\Rightarrow\ (x-8)(x+3)=0`

Answer 2

x² - 5x - 24 = 0

x² ⇒ x * x ⇒ (x + __) (x - __)
24 ⇒ 8 * 3
-5 ⇒ - 8 + 3

(x - 8)(x + 3) = 0

x(x+3) - 8(x+3) = x² + 3x - 8x - 24 = x² - 5x - 24

(x-8) = 0
x = 8

(x+3) = 0
x = -3