Question

question 5 (4 points) find the discriminant, then by knowing the discriminant, state the number of solutions and the type of solution for the given quadratic equation. upload your handwritten work displaying how you solved the problem. ( f(x) = 2x^2 - 4x + 1 )

Explanation:

Step1: Identify quadratic coefficients

For $f(x)=2x^2-4x+1$, $a=2$, $b=-4$, $c=1$

Step2: Calculate discriminant

Use formula $\Delta = b^2-4ac$
$\Delta = (-4)^2 - 4(2)(1) = 16 - 8 = 8$

Step3: Classify solution type

Since $\Delta>0$, there are 2 distinct real solutions.

Step4: Solve quadratic equation

Use quadratic formula $x=\frac{-b\pm\sqrt{\Delta}}{2a}$
$x=\frac{4\pm\sqrt{8}}{2(2)}=\frac{4\pm2\sqrt{2}}{4}=\frac{2\pm\sqrt{2}}{2}$

Answer:

Discriminant: $8$
Number/type of solutions: 2 distinct real solutions
Solutions: $x=\frac{2+\sqrt{2}}{2}$ and $x=\frac{2-\sqrt{2}}{2}$