Question

solve each equation. $5y^2 - 7y + 1 = 0$

Explanation:

Step1: Identify coefficients for quadratic formula

For the quadratic equation \(5y^2 - 7y + 1 = 0\), we have \(a = 5\), \(b = -7\), and \(c = 1\). The quadratic formula is \(y=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).

Step2: Calculate the discriminant

First, calculate the discriminant \(D = b^2 - 4ac\). Substitute the values: \(D=(-7)^2 - 4\times5\times1 = 49 - 20 = 29\).

Step3: Apply the quadratic formula

Now, substitute \(a\), \(b\), and \(D\) into the quadratic formula: \(y=\frac{-(-7)\pm\sqrt{29}}{2\times5}=\frac{7\pm\sqrt{29}}{10}\).

Answer:

\(y = \frac{7 + \sqrt{29}}{10}\) or \(y = \frac{7 - \sqrt{29}}{10}\)