Question

3y² + 8y + 5 = 0

Answer 1

We have 3y² + 8y + 5 = 0
On comparing this equation with ay² + by + c = 0, we get:
a = 3, b = 8, c = 5
For the quadratic equation ay² + by + c = 0 in variable y , we know that the quadratic formula is $y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
On substituting a = 3, b = 8, c = 5, we get:

$$\begin{gathered} y=\frac{-8\pm \sqrt{(8{)}^2-4(3\left)\right(5)}}{2\left(3\right)} \\ =\frac{-8\pm \sqrt{64-60}}{6} \\ =\frac{-8\pm \sqrt{4}}{6} \\ =\frac{-8\pm 2}{6} \\ =\frac{-8+2}{6},\frac{-8-2}{6} \\ =-1,-\frac{5}{3} \end{gathered}$$

Thus, the solution of the given quadratic equation is y = $-1,-\frac{5}{3}$.