Question

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

Two rational solutions
One rational solution
Two irrational solutions
Two complex solutions

Answer 1

Two rational real solutions -8 & +8

Answer 2

The type of solutions is:

• Two rational solutions.

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=(-b\pm √(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=(-(-2)\pm √((-2)^2-4* 5* (-3)))/(2* 5)\\\\i.e.\\\\x=(2\pm √(4+60))/(10)\\\\i.e.\\\\x=(2\pm √(64))/(10)\\\\i.e.\\\\x=(2\pm 8)/(10)\\\\i.e.\\\\x=(2+8)/(10)\ and\ x=(2-8)/(10)\\\\i.e.\\\\x=(10)/(10)\ and\ x=(-6)/(10)\\\\x=1\ and\ x=(-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)