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To find the x-intercepts of the graph of the quadratic equation y = 2x² + 5x + 9, you need to consider the discriminant of the quadratic formula. The discriminant is given by the formula: Δ = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c.
In this case, the equation y = 2x² + 5x + 9 has coefficients a = 2, b = 5, and c = 9. Calculating the discriminant:
Δ = 5² - 4*2*9
Δ = 25 - 72
Δ = -47
Since the discriminant is negative (Δ < 0), the quadratic equation has no x-intercepts. Therefore, the correct answer is:
B. 0
If the discriminant were equal to zero (Δ = 0), the quadratic equation would have one real x-intercept. If the discriminant were positive (Δ > 0), the quadratic equation would have two distinct real x-intercepts.
