Answer:
The type of solutions is:
Step-by-step explanation:
The trinomial expression is given by:
[tex]5x^2-2x-3[/tex]
The solution is the possible values of x where the expression is equal to 0.
i.e.
[tex]5x^2-2x-3=0[/tex]
On solving the equation using quadratic formula.
i.e. any quadratic equation of the form:
[tex]ax^2+bx=c=0[/tex]
has the solution of the type:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
On comparing our equation with the general quadratic equation we have:
a=5 , b= -2 and c= -3
Hence, the solution is given by:
[tex]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}[/tex]
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)
