f(x) = 3x^2 + 5x + C . Find C if f(x) has two complex roots and C is an integer greater than 1.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The function f(x) = 3x^2 + 5x + C has two complex roots and C is an integer greater than 1.

A quadratic function of the form ax^2 + bx + c has complex roots if b^2 < 4ac

Substituting the values we have

5^2 < 4*3*C

=> 25 < 12C

=> 25/12 < C

25/12 is equal to 2.0833

But C is an integer greater than 1. So it can take on any integer value greater can 2.

The value of C lies in [3, inf.)

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the quadratic equation :

f(x) = 3x^2 + 5x + C

We know that f(x) has two complex roots.

Then the discriminant is negative.

==> (b^2 - 4ac < 0

a = 3   b= 5   c = C

==> 25 - 4*3*C < 0

==> 25 - 12C < 0

==> 25 < 12 C

==> 25/12 < C

==> 2.08 < C

But we know that C is an integer greater than 1.

==>  C = { 3, 4, 5, ....}

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