Answer:
Option a, two rational solutions.
Step-by-step explanation:
It is given the trinomial as
[tex]5x^2-2x-3[/tex]
This is a quadratic equation in standard form.
To find the nature of roots let us analyse the discriminant.
Discriminant of the quadratic equation
=[tex]b^2-4ac\\=(-2)^2-4(-3)(5)\\=4+60\\=64[/tex]
Since discriminant is a perfect square, we see that the roots will be rational.
Hence two rational solutions is the answer.
The solution of the trinomial is Two rational solutions since we can express the solutions as a ratio of two integers.
Given the quadratic equation 5x² − 2x − 3
Factorize the quadratic equation
Let f(x) = 0
5x² − 2x − 3 = 0
5x² -5x + 3x - 3 = 0
5x(x-1)+1(x-1) = 0
(5x+1)(x-1) = 0
5x+1 = 0 and x-1 = 0
5x = -1 and x = 1
x = -1/5 and x = 1
Hence the solution of the trinomial is Two rational solutions since we can express the solutions as a ratio of two integers.
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