+find the discriminant and the number of real roots for this equation 9x^2+12x+14
2 answers:
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<u>Given</u>:
The given function is
We need to determine the value of the discriminant f and also to determine the distinct real number zeros of f.
<u>Discriminant</u>:
The discriminant can be determined using the formula,
Now, we shall determine the discriminant of the function
Substituting the values in the formula, we have;
Thus, the value of the discriminant of f is -92.
<u>Distinct roots:</u>
The distinct zeros of the function f can be determined by
(1) If , then the function has 2 real roots.
(2) If , then the function has 2 real roots ( or one repeated root).
(3) If , then the function has 2 imaginary roots (or no real roots).
Since, the discriminant is , then the function has no real roots or 2 imaginary roots.
Thus, the function has 2 imaginary roots.