Question

2n² + 5n + 2 = 0

Answer 1

Given: 2n² + 5n + 2 = 0
On comparing this equation with ax² + bx + c = 0, we get:
a = 2, b = 5 and c = 2
Here, the given equation is a quadratic equation in variable n.

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 = 2, b = 5 and c = 2, we get:

$$\begin{gathered} n=\frac{-5\pm \sqrt{5^2-4\times 2\times 2}}{2\times 2} \\ =\frac{-5\pm \sqrt{25-16}}{4} \\ =\frac{-5\pm \sqrt{9}}{4} \\ =\frac{-5\pm 3}{4} \\ =\frac{-5+3}{4},\frac{-5-3}{2} \\ =\frac{-2}{4},\frac{-8}{4} \\ =\frac{-1}{2},-2 \end{gathered}$$

Thus, the solution of the given quadratic equation is n = $\frac{-1}{2},-2$.