Question

How many x-intercepts does the graph of y = 4x2 + 5x + 2 have?
Previous
This graph has
choose your answer... ^ x-intercepts. choose your answer...
two
no
one

Answer 1

To determine the number of x-intercepts of the graph given by the equation \( y = 4x^2 + 5x + 2 \), we can use the discriminant from the quadratic formula \( ax^2 + bx + c = 0 \).

The discriminant \( D \) is given by:

\[
D = b^2 - 4ac
\]

For the equation \( 4x^2 + 5x + 2 \):

- \( a = 4 \)
- \( b = 5 \)
- \( c = 2 \)

Now we can calculate the discriminant:

\[
D = 5^2 - 4 \cdot 4 \cdot 2
\]
\[
D = 25 - 32
\]
\[
D = -7
\]

Since the discriminant is negative \( (D < 0) \), this means that the quadratic equation has no real roots. Therefore, the graph of the equation \( y = 4x^2 + 5x + 2 \) has **no x-intercepts**.

So the answer is: **no**.