How many real number solutions does this equation have?
0= 5x^2 +2x - 12
one, two none, or infinite
How many real number solutions does this equation have?
0= 2x^3 - 20x + 50
If the discriminant is negative no real solution exists.
If the discriminant is equal to 0 only one real solution exists.
If the discriminant is positive 2 real solutions exist.
The discriminant:
D = b² - 4 ac
0= 5x^2 +2x - 12
here a = 5, b = 2, c = -12
D = b² - 4 ac
D = (2)^2 - 4 (5)(-12) = 244
Since the discriminant is positive, 2 real solutions exist.
0= 2x^3 - 20x + 50
here a=2, b=-20, c=50
D = b² - 4 ac
D =(-20)^2 - 4(2)(50) = 0
Since the discriminant is equal to 0 only one real solution exists.
oh thanks, that little guide at the top makes a lot more sense than the way my teacher explained it. THANKS!!!
formula: -b±√b^2 -4ac
____________
2a
Oh, it's equation-solving time! Let's see what we've got here:
For the first equation, 0= 5x^2 +2x - 12, the number of real number solutions could be one, two, none, or even infinite! But don't worry, I won't leave you hanging like a trapeze artist without a safety net. To find out how many solutions there are, we can use the quadratic formula or try factoring the equation.
As for the second equation, 0= 2x^3 - 20x + 50, it's a cubic equation. Brace yourself for some more complex numbers to juggle! Again, it could have one, two, none, or infinite real number solutions.
But hey, if you want a quick and funny answer, just pretend the real numbers are hiding in the circus and playing peek-a-boo with the solutions. Keep searching, and you'll find out soon enough!
To determine the number of real number solutions for each equation, we can use the discriminant. The discriminant is the part of the quadratic formula that is located under the square root symbol (√). For a quadratic equation in the form ax^2 + bx + c = 0, the discriminant is given by b^2 - 4ac.
Let's solve each equation separately to find the discriminant and determine the number of real solutions:
1. Equation: 0 = 5x^2 + 2x - 12
Here, a = 5, b = 2, and c = -12.
The discriminant (D) = b^2 - 4ac = 2^2 - 4(5)(-12) = 4 + 240 = 244
Since the discriminant is positive (244 > 0), there are two real number solutions for this equation.
Therefore, the equation 0 = 5x^2 + 2x - 12 has two real number solutions.
2. Equation: 0 = 2x^3 - 20x + 50
Here, a = 2, b = 0, and c = 50.
The discriminant (D) = b^2 - 4ac = 0^2 - 4(2)(50) = 0 - 400 = -400
Since the discriminant is negative (-400 < 0), there are no real number solutions for this equation.
Therefore, the equation 0 = 2x^3 - 20x + 50 has no real number solutions.
1. 5x^2+2x-12 = 0.
h = Xv = -B/2A = -2/10 = -0.2.
K = 5*(-0.2)^2 + 2*(-0.2)-12 = -12.2.
V(h, k) = V(-0.2, -12.2).
k < 0. Therefore, we have 2 solutions.
k = 0. One solution.
k > 0. No solutions.