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

Sagot :

The given expression is

[tex]x^2-5x+2=-4x+5[/tex]

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

[tex]x^2-5x+4x+2-5=0[/tex]

Then, we reduce like terms

[tex]x^2-x-3=0[/tex]

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

[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]

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

[tex]\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}[/tex]

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

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