Considering it's discriminant, it is found that:
A. The classmate is wrong, as the discriminant is of zero, hence the equation has one solution.
B. The quadratic equation has 1 x-intercept.
What is the discriminant of a quadratic equation and how does it influence the solutions?
A quadratic equation is modeled by:
y = ax^2 + bx + c
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
- If [tex]\mathbf{\Delta > 0}[/tex], it has 2 real solutions.
- If [tex]\mathbf{\Delta = 0}[/tex], it has 1 real solutions.
- If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.
In this problem, the equation is:
y = 9x² - 6x + 1.
The coefficients are a = 9, b = -6 and c = 1, hence the discriminant is:
[tex]\Delta =(-6)^2 - 4(9)(1) = 36 - 36 = 0[/tex]
Since the discriminant is zero, the classmate is wrong, as it means that the equation has one solution = one x-intercept.
More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811
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