Question

Given the trinomial 5x2 - 2x - 3, predict the type of solutions.

Answer 1

Two rational real solutions -8 & +8

Answer 2

Answer:

The type of solutions is:

•    Two rational solutions.

Step-by-step explanation:

The trinomial expression is given by:

$5x^2-2x-3$

The solution is the possible values of x where the expression is equal to 0.

i.e.

$5x^2-2x-3=0$

On solving the equation using quadratic formula.

i.e. any quadratic equation of the form:

$ax^2+bx=c=0$

has the solution of the type:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

On comparing our equation with the general quadratic equation we have:

a=5 , b= -2 and c= -3

Hence, the solution is given by:

$x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4\times 5\times (-3)}}{2\times 5}\\\\i.e.\\\\x=\dfrac{2\pm \sqrt{4+60}}{10}\\\\i.e.\\\\x=\dfrac{2\pm \sqrt{64}}{10}\\\\i.e.\\\\x=\dfrac{2\pm 8}{10}\\\\i.e.\\\\x=\dfrac{2+8}{10}\ and\ x=\dfrac{2-8}{10}\\\\i.e.\\\\x=\dfrac{10}{10}\ and\ x=\dfrac{-6}{10}\\\\x=1\ and\ x=\dfrac{-3}{5}$

Hence, we get that both the solutions are rational solutions.

( Since  a rational number is a number which could be represented in the form of p/q where p belongs to integers and q belongs to natural numbers)