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Answers:
A) d = 2
B) x = 1/2
Why?
We have dx2 + 5x - 3 = 0, and one solution is x = -3.
The equation is quadratic, so it can be factored into two linear terms (things that look like ax+b). Since,
x = -3
x + 3 = -3 +3
x + 3 = 0
So x + 3 is one of the terms.
So dx2 + 5x - 3 = 0 is equivalent to
(?x + ?)(x + 3) = 0
The first ? must be d since ?x*x = dx2. The second ? must be -1 since ?*3 = -3.
So we have
(dx - 1)(x + 3) = 0
When we distribute (students often know as F.O.I.L.), we find that
dx2+ 3dx - x - 3 = 0
dx2+ (3d-1)x - 3 = 0 (factor out x, or think of combining like terms) This is the same as:
dx2 + 5x - 3 = 0 So we know 3d - 1 = 5, an equation we can solve for d.
3d - 1 = 5
3d - 1 + 1 = 5 + 1
3d = 6
3d/3 = 6/3
d = 2
Yay! Part A of your problem is complete: d = 2.
Next, Part B, we must find the other root, or solution.
So now we have
2x2 + 5x - 3 = 0 is the same as
(2x - 1)(x + 3) = 0 so we know
2x - 1 = 0
2x - 1 + 1 = 0 + 1
2x = 1
2x/2 = 1/2
x = 1/2
So for Part B, we have x = 1/2 is the other root.
What else can I help you with?
What is the discriminant of an algebra equation?
I am assuming that "an algebra equation" refers to a quadratic equation and not a higher polynomial.For a quadratic equation of the form y = ax^2 + bx + c, where a, b and c are real numbers and a is non-zero, the discriminant is b^2 – 4ac.
When must the quadratic formula be used in algebra?
You'll typically use it when solving a quadratic equation - when factoring isn't obvious.
What word in algebra is used to determine the number of x-intercepts a quadratic has?
These are the real ROOTS of the quadratic equation when it equals zero. Example : x2- 7x + 10 = 0 can be written as (x - 5)(x - 2) = 0 Then x = 5 and x = 2 are the roots of this equation.
Why the discriminant of a quadratic is useful in algebra?
Because the square root of the discriminant is a component of the roots of the equation.
How can apply quadratic equations in your life?
It really depends what you work in; if you work in science, or in engineering (applied science), you will need the quadratic equation - and a lot more advanced math as well. Examples that involve the quadratic equation are found in abundance in algebra textbooks; for example, an object in free fall.
What is the discriminant of an algebra equation?
I am assuming that "an algebra equation" refers to a quadratic equation and not a higher polynomial.For a quadratic equation of the form y = ax^2 + bx + c, where a, b and c are real numbers and a is non-zero, the discriminant is b^2 – 4ac.
What does it mean in algebra to complete the square?
A quadratic equation can be solved by completing the square which gives more information about the properties of the parabola than with the quadratic equation formula.
When must the quadratic formula be used in algebra?
You'll typically use it when solving a quadratic equation - when factoring isn't obvious.
What word in algebra is used to determine the number of x-intercepts a quadratic has?
These are the real ROOTS of the quadratic equation when it equals zero. Example : x2- 7x + 10 = 0 can be written as (x - 5)(x - 2) = 0 Then x = 5 and x = 2 are the roots of this equation.
Derive the quadratic formula?
If you know how to complete the square, this link will finish the job for you. http://www.mathsisfun.com/algebra/quadratic-equation-derivation.html
Why the discriminant of a quadratic is useful in algebra?
Because the square root of the discriminant is a component of the roots of the equation.
How do you determine the solutions on a graph for a quadratic equation?
The X-Intercepts are the solutions. If you have an algebra calculator, you can usually find them by going to CALC>Zero>enter the left and right boundaries for each side.
What is Factor-Factorproduct relationship?
The Factor-Factor Product Relationship is a concept in algebra that relates the factors of a quadratic equation to the roots or solutions of the equation. It states that if a quadratic equation can be factored into the form (x - a)(x - b), then the roots of the equation are the values of 'a' and 'b'. This relationship is crucial in solving quadratic equations and understanding the behavior of their roots.
How can apply quadratic equations in your life?
It really depends what you work in; if you work in science, or in engineering (applied science), you will need the quadratic equation - and a lot more advanced math as well. Examples that involve the quadratic equation are found in abundance in algebra textbooks; for example, an object in free fall.
What is the minimum or maximum point called in a quadratic equation?
They are simply referred to as local minimums and maximums. Experience: Algebra 2 Advanced
How do you plot the graph of a quadratic equation?
Just like any other equation, you can set up a table of x values, and calculate the corresponding y values. Then plot the points on the graph. In this case, it helps to have some familiarity with quadratic equations (you can find a discussion in algebra books), and recognize (from the form of the equation) whether your quadratic equation represents a parabola, a circle, an ellipse, or a hyperbola.
How do you solve for x?
Solving for any variable in an equation differs from equation to equation. You can use various methods such as the quadratic formula, factoring, brute force algebra etc.ExampleSolve x in the the equation logx8=3/2 Answer(5(root(10)))/4
