Question

9p² – 5p – 4 = 0

Answer 1

Given: 9p² – 5p – 4 = 0
On comparing this equation with ap² + bp + c = 0, we get:
a = 9, b = –5, c = –4
For the quadratic equation ap² + bp + c = 0 in variable p, we know that the quadratic formula is $p=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
On substituting a = 9, b = –5, c = –4, we get:

$$\begin{gathered} p=\frac{-(-5)\pm \sqrt{(-5{)}^2-4(9\left)\right(-4)}}{2\left(9\right)} \\ =\frac{5\pm \sqrt{25+144}}{18}=\frac{5\pm \sqrt{169}}{18}=\frac{5\pm 13}{18}=\frac{18}{18},\frac{-8}{18}=1,\frac{-4}{9} \end{gathered}$$

Thus, the solution of the given quadratic equation is $p=1,-\frac{4}{9}$.