Question

7p² – 5p – 2 = 0

Answer 1

Given: 7p² – 5p – 2 = 0
On comparing this equation with ax² + bx + c = 0, we get:
a = 7, b = –5 and c = –2
Here, the variable of the quadratic equation is p.
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 = 7, b = –5 and c = –2, we get:
$$\begin{gathered} p=\frac{-\left(-5\right)\pm \sqrt{{\left(-5\right)}^2-4\times 7\times \left(-2\right)}}{2\times 7} \\ =\frac{5\pm \sqrt{25+56}}{14} \\ =\frac{5\pm \sqrt{81}}{14} \\ =\frac{5\pm 9}{14} \\ =\frac{5+9}{14},\frac{5-9}{14} \\ =\frac{14}{14},\frac{-4}{14} \\ =1,\frac{-2}{7} \end{gathered}$$
Thus, the solution of the given quadratic equation is p = $1,\frac{-2}{7}$.