How many real number solutions does the equation have?
y=-4x^2+7x-8
A. no solutions
B. one solution
C. two solutions
D. infinitely many solutions
I think it is C..?
How many real number solutions does the equation have?
y=2x^2-20x+50
A. no solutions
B. one solution
C. two solutions
D. infinitely many solutions
I think it is B..?
check the discriminant
#1: b^2-4ac < 0, so no solutions
#2: b^2-4ac = 0, so one solution
Thank you
To determine the number of real number solutions for each equation, we can use the discriminant of the quadratic equations. The discriminant is given by b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.
1. For the equation y = -4x^2 + 7x - 8:
The coefficient of x^2 is a = -4
The coefficient of x is b = 7
The constant term is c = -8
The discriminant is b^2 - 4ac = (7)^2 - 4(-4)(-8) = 49 - 128 = -79
Since the discriminant is negative (-79), the equation has no real number solutions.
Therefore, the correct answer is A. no solutions.
2. For the equation y = 2x^2 - 20x + 50:
The coefficient of x^2 is a = 2
The coefficient of x is b = -20
The constant term is c = 50
The discriminant is b^2 - 4ac = (-20)^2 - 4(2)(50) = 400 - 400 = 0
Since the discriminant is zero (0), the equation has exactly one real number solution.
Therefore, the correct answer is B. one solution.
To determine the number of real number solutions for each equation, we can use the discriminant of the quadratic equation of the form ax^2 + bx + c = 0. The discriminant is given by the expression b^2 - 4ac.
For the equation y = -4x^2 + 7x - 8, we can compare it with the standard quadratic equation form ax^2 + bx + c = 0 and find that a = -4, b = 7, and c = -8. Now, calculate the discriminant:
b^2 - 4ac = (7)^2 - 4(-4)(-8) = 49 - 128 = -79
Since the discriminant is negative (-79), there are no real solutions for this equation. Therefore, the correct answer is A. no solutions.
For the equation y = 2x^2 - 20x + 50, we can again compare it with the standard quadratic equation form ax^2 + bx + c = 0 and find that a = 2, b = -20, and c = 50. Now, calculate the discriminant:
b^2 - 4ac = (-20)^2 - 4(2)(50) = 400 - 400 = 0
Since the discriminant is zero (0), there is exactly one real solution for this equation. Therefore, the correct answer is B. one solution.