Find the number of irrational roots of the equation <mstyle displaystyle="true" scriptlevel="0">

Akira Huang

Akira Huang

Answered question

2022-05-23

Find the number of irrational roots of the equation
4 x x 2 + x + 3 + 5 x x 2 5 x + 3 = 3 2 .

Answer & Explanation

Dreforganzv

Dreforganzv

Beginner2022-05-24Added 9 answers

We start by shifting the 2 nd term on LHS of the given identity to its RHS.
4 x x 2 + x + 3 = 3 2 5 x x 2 5 x + 3
When RHS is simplified, we have,
4 x x 2 + x + 3 = 3 x 2 5 x + 9 2 x 2 10 x + 6 .
Now, we add the denominators to the respective numerators to get,
x 2 + 5 x + 3 x 2 + x + 3 = x 2 5 x 3 2 x 2 10 x + 6 .
This implies,
x 2 + 5 x + 3 = 0 and x 2 + x + 3 = 2 x 2 + 10 x 6 x 2 3 x + 3 = 0.
The first quadratic equation gives us two irrational roots, while the second two imaginary roots

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