Question

Use the discriminant, b^2 - 4ac, to determine the number of solutions of the following quadratic equation. -7y^2 + 7y = 1Then solve the quadratic equation using the formula Y = (formula to use is in the picture attached)

Answer 1

Answers:

`\begin{gathered} y=\frac{7-\sqrt[]{21}}{14} \\ or \\ y=\frac{7+\sqrt[]{21}}{14} \end{gathered}`

Step-by-step explanation:

To use the quadratic formula, the equation should have the following form:

`ax^2+bx+c=0`

So, a is the number beside the y^2, b is the number beside y and c is the constant value.

Then, subtracting 1 from both sides of the equation, we get:

`\begin{gathered} -7y^2+7y=1 \\ -7y^2+7y-1=1-1 \\ -7y^2+7y-1=0 \end{gathered}`

Therefore, the value of a is -7, the value of b is 7 and the value of c is -1. So, the discriminant is equal to:

`\begin{gathered} b^2-4ac=7^2-4(-7)(-1) \\ b^2-4ac=49-28 \\ b^2-4ac=21 \end{gathered}`

Since the value of the discriminant is positive, we have two different real solutions. So, we can solve the quadratic equation as follows:

`\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y=\frac{-7_{}\pm\sqrt[]{21}}{2(-7)}=\frac{-7\pm\sqrt[]{21}}{-14} \end{gathered}`

Therefore, the solutions of the equation are:

`\begin{gathered} y=\frac{-7+\sqrt[]{21}}{-14}=\frac{7-\sqrt[]{21}}{14} \\ or \\ y=\frac{-7-\sqrt[]{21}}{-14}=\frac{7+\sqrt[]{21}}{14} \end{gathered}`