The x intercepts are the zeros of the function, the roots of the equation
[tex]4x^2 + 5x + 2 = 0[/tex]
The discriminant is
[tex]d=b^2 - 4ac = 5^2 - 4 (4)(2) = 25 - 32 = -7[/tex]
That's negative, so the answer is no zeros, choice B.
The other way to see it is to complete the square:
[tex]y = 4x^2 + 5x + 2 = 4(x^2 + \frac 5 4 x) + 2[/tex]
[tex]y = 4(x^2 + \frac 5 4 x + (\frac 5 8)^2) - 4 (\frac 5 8)^2+2 = 4(x + \frac 5 8)^2 + \frac{7}{16}[/tex]
The minimum of that function is clearly a positive 7/16, so the function never crosses zero.
