Question

solve the equation: $5k^{2}-7k + 2 = 0$. fully simplify all answers, including non - real solutions.
k =
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Explanation:

Step1: Identify quadratic coefficients

For $5k^2 -7k +2=0$, $a=5$, $b=-7$, $c=2$

Step2: Apply quadratic formula

$$k=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Compute discriminant

$\Delta=(-7)^2-4(5)(2)=49-40=9$

Step4: Substitute and simplify

$$k=\frac{7\pm\sqrt{9}}{10}=\frac{7\pm3}{10}$$

Step5: Calculate two solutions

$k_1=\frac{7+3}{10}=1$, $k_2=\frac{7-3}{10}=\frac{4}{10}=\frac{2}{5}$

Answer:

$k=1$ and $k=\frac{2}{5}$