For what values of m does the graph of y = 3x^2 + 7x + m have two x-intercepts?
Answer: The graph of y = 3x^2 + 7x + m has two x-intercepts if the discriminant of the quadratic equation, which is b^2 – 4ac, is greater than 0. Here a = 3, b = 7, and c = m. So, 7^2 – 43m > 0. This simplifies to m < 49/12.
Quadratic Equations
The discriminant of a quadratic equation is given by the formula b^2 – 4ac. If the discriminant is greater than 0, the quadratic equation has two distinct real roots. If the discriminant is equal to 0, the equation has one real root. If the discriminant is less than 0, the equation has no real roots, only complex roots.
FAQ on Quadratic Equations
What is a quadratic equation?
A quadratic equation is an equation that can be written in the form ax^2 + bx + c = 0, where a ≠ 0.
What is the quadratic formula?
The quadratic formula is x = [-b ± sqrt(b^2 – 4ac)] / (2a), which can be used to find the roots of a quadratic equation.
What is a root or zero of a quadratic equation?
A root or zero of a quadratic equation is a value of x that makes the equation equal to zero.
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