Question

12. Given the quadratic function f(x) = 4x² +7x+c, where c is some real number constant.

(a) If c = 3, are the zeroes of f(x) rational or irrational numbers? Explain how you arrived at your choice.
[3 points]

(b) Determine all values of c for which the graph of y=f(x) will have no x-intercepts. Show all work.
[3 points]

Answer 1

Explanation:

A.Rational because by using the discrmant formula, Since our coefficients are integers, and if we get a perfect square, inside a radicand , we will have a rational numbers.

For example:

`\sqrt{ {7}^(2) - 4(4)(3) } = √(49 - 48) = √(1) = 1`

Since root 1, is a perfect square, we will have rational roots.

B.

`{b}^(2) - 4ac < 0`

`49 - 16c < 0`

`- 16c < - 49`

`c > (49)/(16)`

If c is greater than 49/16, we will have no x intercepts.