Chapter 4.4, Problem 79E

To determine

To solve: the given quadratic equation by factorization.

Answer to Problem 79E

The solution of the given equation is $x=\frac{5}{3},x=2$ .

Explanation of Solution

Given information:

A quadratic equation is given as

  $3x^2-11x+10=0$

Calculation:

Consider the given equation.

  $3x^2-11x+10=0$

Now, break the coefficient of middle term $-11$ as sum or difference of two numbers such that product of the numbers is equal to the product of first term and constant term that is product of $3$ and $10$ .

Such numbers will be $-5$ and $-6$ .

Now, factorize left side of $3x^2-11x+10=0$ as shown:

  $\begin{array}{c}3x^2-11x+10=0\\ 3x^2-5x-6x+10=0\\ x\left(3x-5\right)-2\left(3x-5\right)=0\\ \left(3x-5\right)\left(x-2\right)=0\end{array}$

Solution can be found by equating each factor with 0.

  $\begin{array}{c}3x-5=0\\ x=\frac{5}{3}\end{array}$ and $\begin{array}{c}x-2=0\\ x=2\end{array}$

Therefore, the solution of the given equation is $x=\frac{5}{3},x=2$ .