Question

Consider the following quadratic equation:35x2 = 13x + 12Step 1 of 2: Using the standard form ax² + bx + c = 0 of the given quadratic equation, factor theleft hand side of the equation into two linear factors.AnswerKeypadKeyboard Shortcuts= 0

Answer 1

Given: The quadratic equation below

`35x^2=13x+12`

To Determine: The two linear factors of the given equation using standard form of a quadratic equation

The standard form of a quadratic equation is given as

`ax^2+bx+c=0`

Re-write the given equation in the standard form as shown below

`\begin{gathered} 35x^2=13x+12 \\ 35x^2-13x-12=0 \end{gathered}`

Factor the left hand side as shown below

`35x^2-28x+15x-12=0`
`\begin{gathered} 7x(5x-4)+3(5x-4)=0 \\ (5x-4)(7x+3)=0 \\ \text{Therefore} \\ 35x^2-13x-12=0,in\text{ factored form is} \\ (5x-4)(7x+3)=0 \end{gathered}`

Hence, the two linear factors of the given equation is

(5x -4)(7x + 3) = 0