Question

2. Identify the x intercepts of: x^2 - 5x + 2 = -4x + 5

Answer 1

The given expression is

`x^2-5x+2=-4x+5`

First, let's move all the terms to the left side

`x^2-5x+4x+2-5=0`

Then, we reduce like terms

`x^2-x-3=0`

To find the x-intercepts, we use the quadratic formula

`x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Where a = 1, b = -1, and c = -3. Let's replace these values

`\begin{gathered} x_(1,2)=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(1)(-3)}}{2(1)}_{} \\ x_(1,2)=\frac{1\pm\sqrt[]{1+12}}{2}=\frac{1\pm\sqrt[]{13}}{2} \\ x_1=\frac{1+\sqrt[]{13}}{2}\approx2.3 \\ x_2=\frac{1-\sqrt[]{13}}{2}\approx-1.3 \end{gathered}`

Hence, the x-intercepts are (2.3, 0) and (-1.3, 0).