Question

Show all work to solve 3x^2 − 5x − 2 = 0

Answer 1

Answer:

x=2

Step-by-step explanation:

Step 1: Factor left side of equation.

(3x+1)(x−2)=0

Step 2: Set factors equal to 0.

3x+1=0 or x−2=0

Answer 2

The solution of quadratic equation $3 x^{2}-5 x-2=0$ is $x=2 \text { or } \frac{-1}{3}$

Solution:

Given, equation is $3 x^{2}-5 x-2=0$

We have to solve the above given quadratic equation.

Now, take the given quadratic equation  

$\rightarrow 3 x^{2}-5 x-2=0$

Splitting “-5x” as -6x + x

$\rightarrow 3 x^{2}-6 x+x-2=0$

Take “3x” as common term from first two terms

$\rightarrow 3 x(x-2)+1(x-2)=0$

Take (x - 2) as common

$\rightarrow(x-2)(3 x+1)=0$

Equating to zero we get,

$\begin{array}{l}{\rightarrow x-2=0 \text { or } 3 x+1=0} \\\\ {\rightarrow x=2 \text { or } 3 x=-1} \\\\ {\rightarrow x=2 \text { or } x=\frac{-1}{3}} \\\\ {\rightarrow x=2 \text { or } \frac{-1}{3}}\end{array}$

Hence, the roots the quadratic equation are 2 and $\frac{-1}{3}$