Use the discriminant to determine how many real-number solutions the equation has.
v2 - 7v + 5 = 0
You must mean the quadratic equation,
v^2 -7v +5 = 0
The discriminant is b^2 - 4ac = 49 - 20 = 29
Since this is positive, there are two real answers, [7 +/- sqrt29]/2
which are 6.1936 and 0.8074
To determine the number of real-number solutions of a quadratic equation, we can use the discriminant. The discriminant is calculated using the formula:
b^2 - 4ac
where the quadratic equation is in the form ax^2 + bx + c = 0.
In this case, the quadratic equation is v^2 - 7v + 5 = 0. Comparing it to the standard form, we can see that a = 1, b = -7, and c = 5.
Now, let's calculate the discriminant using the formula:
Discriminant = b^2 - 4ac
Plugging in the values, we have:
Discriminant = (-7)^2 - 4(1)(5)
Discriminant = 49 - 20
Discriminant = 29
The discriminant for this equation is 29.
To determine the number of real-number solutions, we can interpret the value of the discriminant as follows:
1. If the discriminant is positive (greater than 0), the quadratic equation has two distinct real solutions.
2. If the discriminant is zero, the quadratic equation has one real solution (a repeated root).
3. If the discriminant is negative (less than 0), the quadratic equation has no real solutions (only complex solutions).
In our case, the discriminant is positive (29). Therefore, the equation v^2 - 7v + 5 = 0 has two distinct real solutions.