-7x^2+6x+3=0
how many real number solutions does the equation have
can you explain it by doing it...i don't get it...baby steps please
thank you
-7x^2+6x+3 = 0.
h = Xv = -B/2A = -6/-14 = 3/7 = .
k = Yv = -7(3/7)^2 + 6(3/7) + 3 = -9/7 + 18/7 + 21/7 = 30/7 = 4.3.
V(h, k) = V(0.43, 4.3).
For a parabola that opens downward:
k < o. No real solution.
k = 0. 1 real solution.
k > 0. 2 real solutions.
Sure, let's break it down step by step!
First, we have the equation: -7x^2 + 6x + 3 = 0
To find the number of real number solutions, we can use the discriminant. The discriminant is the term under the square root in the quadratic formula, which is b^2 - 4ac.
In this case, the equation is in the form ax^2 + bx + c = 0, where a = -7, b = 6, and c = 3.
Now, let's calculate the discriminant:
b^2 - 4ac
(6)^2 - 4(-7)(3)
36 + 84
120
Since the discriminant is positive (greater than zero), it means there are two distinct real number solutions.
So, the equation has 2 real number solutions.
I hope this helps! If you have any more questions, feel free to ask!
To determine the number of real number solutions of the equation -7x^2 + 6x + 3 = 0, we can use the discriminant. The discriminant is the expression b^2 - 4ac, where a, b, and c are coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this case, a = -7, b = 6, and c = 3. Let's substitute these values into the discriminant formula:
Discriminant = b^2 - 4ac
= (6)^2 - 4(-7)(3)
= 36 + 84
= 120
The discriminant is positive (120 > 0). When the discriminant is positive, the quadratic equation has two distinct real number solutions.
So, the equation -7x^2 + 6x + 3 = 0 has two real number solutions.
Sure, I'd be happy to help you step by step!
Step 1: Begin with the given quadratic equation: -7x^2 + 6x + 3 = 0.
Step 2: First, we need to determine the discriminant, which is the expression inside the square root in the quadratic formula. The discriminant is given by the formula: D = b^2 - 4ac. In this equation, a = -7, b = 6, and c = 3.
Step 3: Substitute the values of a, b, and c into the formula for the discriminant to find its value: D = (6)^2 - 4(-7)(3).
Step 4: Simplify the expression: D = 36 + 84.
Step 5: Continue simplifying: D = 120.
Step 6: Now, we can interpret the value of the discriminant. If the discriminant is positive, the quadratic equation has two distinct real number solutions. If the discriminant is zero, the equation has one real number solution. And if the discriminant is negative, the equation has no real number solutions.
Step 7: Since the discriminant in this case is positive (D = 120), the quadratic equation -7x^2 + 6x + 3 = 0 has two distinct real number solutions.
In summary, the given quadratic equation has two real number solutions.
the discriminant (b^2 - 4 a c) shows the nature of the roots (solutions)
6^2 - (4 * -7 * 3) = 36 - -84 = 120
a positive discriminant means two real roots