Final answer:
To find the values of m for which the quadratic equation y = 3x² + 7x + m has two x-intercepts, we need to determine the discriminant of the equation, which is given by Δ = b² - 4ac. The discriminant needs to be greater than zero for the equation to have two x-intercepts. Therefore, m < 49/12.
Step-by-step explanation:
To find the values of m for which the quadratic equation y = 3x² + 7x + m has two x-intercepts, we need to determine the discriminant of the equation. The discriminant is given by the formula Δ = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation. In this case, a = 3, b = 7, and c = m.
For the equation to have two x-intercepts, the discriminant needs to be greater than zero, since that indicates two distinct real roots. Therefore, we have:
Δ = 7² - 4(3)(m) > 0
By simplifying the inequality, we get 49 - 12m > 0. Solving for m, we find that m < 49/12. Therefore, the values of m for which the graph of the equation has two x-intercepts are any real numbers less than 49/12.
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