Step-by-step explanation:
Simplifying 4x4 + -12x2 + 8 = 0 Reorder the terms: 8 + -12x2 + 4x4 = 0 Solving 8 + -12x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -3x2 + x4) = 0 Factor a trinomial. 4((1 + -1x2)(2 + -1x2)) = 0 Factor a difference between two squares. 4(((1 + x)(1 + -1x))(2 + -1x2)) = 0 Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1
Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1
Solution
x = {-1.414213562, 1.414213562, -1, 1}
y = ax^2 + 10x + 1
For our graph, y = 0 whenever it crosses the x-axis, so we must solve:
0 = ax^2 + 10x + 1
Using the quadratic formula:
[-10 ± sqrt(100 - 4a)]/(2a)
In order to have two distinct roots, our square root part of the answer above must be a real number that is not zero. In other words:
100 - 4a > 0
Because if the value underneath the square root symbol is negative, we will have no solution, and if the value underneath the square root symbol is zero, then we will only get one solution.
So solve:
100 - 4a > 0
100 > 4a
25 > a
So a must have a value lower than 25. Also note that when a = 0, we have a linear equation which only has one solution that crosses the x-axis, so we must exclude a = 0 as well.
So the answer is:
a < 25, where a ≠ 0
Answer:
i.)12 feet
Step-by-step explanation:
ut+1/2gt^2
7×1+1/2×10×1^2 =12
The factors of the quadratic function are x - 2 and x + 5.
This means the roots of the function are x = 2 and x = -5 and the graph must cross the x-axis at these points
So, we can find the graph by checking which of them is cross the x-axis at points x =2 and x=- 5.
The graph A is crossing the x-axis at the said points.
So the answer to this question is option A