Question

Solving Quadratic Equations by Factoring

Answer 1

Answer:

The required solutions are a. $f(x)=(x-3)(3x+4)$, b. $3\text{ and }-\frac{3}{4}$, c. $3\text{ and }-\frac{3}{4}$.

Step-by-step explanation:

a.

The given quadratic equation is

$f(x)=3x^2-5x-12$

The middle term can be written as (-9x+4x)

$f(x)=3x^2-9x+4x-12$

$f(x)=3x(x-3)+4(x-3)$

$f(x)=(x-3)(3x+4)$

The intercept form of the given equation by factoring. is,

$f(x)=(x-3)(3x+4)$

b.

The x-intercepts,zeros, roots and solutions are same things.

$0=(x-3)(3x+4)$

Equate each factor equal to 0.

$x=3,-\frac{3}{4}$

Therefore x-intercepts,zeros, roots and solutions of the given equation are $3\text{ and }-\frac{3}{4}$.

c.

The given equation is

$3x^2-5x-12=0$

Therefore the solution of the equation are $3\text{ and }-\frac{3}{4}$.