Question

3y² + 7y + 4 = 0

Answer 1

Given: 3y² + 7y + 4 = 0
On comparing this equation with ax² + bx + c = 0, we get:
a = 3, b = 7 and c = 4
The given equation is a quadratic equation in variable y.
For the quadratic equation ax² + bx + c = 0, we know that the quadratic formula is
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
On substituting a = 3, b = 7 and c = 4, we get:
$$\begin{gathered} y=\frac{-7\pm \sqrt{7^2-4\times 3\times 4}}{2\times 3} \\ =\frac{-7\pm \sqrt{49-48}}{6} \\ =\frac{-7\pm \sqrt{1}}{6} \\ =\frac{-7\pm 1}{6} \\ =\frac{-7+1}{6},\frac{-7-1}{6} \\ =\frac{-6}{6},\frac{-8}{6} \\ =-1,\frac{-4}{3} \end{gathered}$$
Thus, the solution of the given quadratic equation is y = $-1,\frac{-4}{3}$.