Question

Use the discriminant, b^2 - 4ac, to determine the number of solutions of the following quadratic equation. y^2 + 14y + 49 = 0Then solve the quadratic equation using the formula Y = (formula is in the picture attached)

Answer 1

The equation:

`y^2+14y+49=0`

has the following values a=1, b=14 and c=49, hence the discriminant is:

`14^2-4(1)(49)=196-196=0`

Since the discriminant is zero we have one solution of multiplicity 2 (this means we have one repeated solution)

Solving the quadratic equation with the general formula:

`\begin{gathered} y=\frac{-14\pm\sqrt[]{14^2-4(1)(49)}}{2(1)} \\ y=\frac{-14\pm\sqrt[]{0}}{2} \\ y=(-14)/(2) \\ y=-7 \end{gathered}`

Therefore the solution is y=-7