how many real-number solutions does the equation have
0 = -7x^2 + 6x + 3
A. One solution
B. Two solutions
C. No solutions
D. Infinite solutions
the discriminant is 36+4*7*3 = 120
what does that tell you?
Erm, one solution?
NO -- stop guessing
The discriminant is called that, because it allows you to discriminate the roots.
For a discriminant of D, recall that x = (-b±√D)/2a
If D=0, there is only one real root (well, two, but they are the same, since you have -b±0)
If D>0 there are two real roots
if D<0 there are two complex roots and no real roots.
All this is there in your book, right?
To find the number of real-number solutions for the given equation, we need to analyze the discriminant of the quadratic equation. The general form of a quadratic equation is given by:
ax^2 + bx + c = 0
In this case, the equation is:
0 = -7x^2 + 6x + 3
Comparing this to the general form, we can see that a = -7, b = 6, and c = 3. The discriminant (D) of a quadratic equation is calculated using the formula:
D = b^2 - 4ac
Substituting the values in, we get:
D = (6)^2 - 4(-7)(3)
Simplifying further:
D = 36 + 84
D = 120
Now, let's analyze the value of the discriminant:
1. If D > 0, the equation has two distinct real-number solutions.
2. If D = 0, the equation has one real-number solution.
3. If D < 0, the equation has no real-number solutions.
In this case, given that D = 120, which is greater than 0, the equation has two real-number solutions.
Therefore, the correct answer is B. Two solutions.