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What else can I help you with?
What are the terms of a quadratic equation?
x equals negative b plus or minus the square root of b squared minus 4bc over 2a
Formula for quadratic equation?
negative b plus or minus the square root of b minus 4 times ac all over 2 a
How do you find maximum height when working with quadratic equations?
In a quadratic equation, the vertex (which will be the maximum value of a negative quadratic and the minimum value of a positive quadratic) is in the exact center of any two x values whose corresponding y values are equal. So, you'd start by solving for x, given any y value in the function's range. Then, you'd solve for y where x equals the middle value of the two x's given in the previous. For example:y = x24 = x2x = 2, -2y = (0)2y = 0Which is, indeed, the vertex of y = x2
A program to compute the real roots of the quadratic equation?
Where the equation is ax2 + bx + c the roots are given by the solutions to : (-b +/- sqrt(b2 - 4ac))/2a So you would first input the values of a, b , and c, then calculate [d = b*b - 4*a*c], and then determine whether it is positive or negative. If it is positive [d>0, or d=0], then you can continue: so the two roots of x are: (-b + sqrt(d))/2/a, and (-b - sqrt(d))/2/a. If d < 0, then you need to calculate sqrt(-d) and then display -b/2/a as the real part, and +/- sqrt(-d)/2/a as the imaginary parts.
The length of the top of the table is 5 m greater that the width The area is 84 m2 Find the dimensions of the table in meters?
7m x 12m (X) x (X+5) = 84 X2 + 5X = 84 X2 + 5X - 84 = 0 Using the Quadratic Equation yields X=(+/- 7) You can't have a negative dimension, so X = 7.
What solution does a negative discriminant have?
In basic mathematics, a quadratic equation with a negative discriminant has no solutions. However, at a more advanced level you will learn that it has two solutions which form a complex conjugate pair.
What type of equation is b2-4ac?
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Does a quadratic equation always have two solutions?
A quadratic equation can have two solutions, one solution, or no real solutions, depending on its discriminant (the part of the quadratic formula under the square root). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is exactly one real solution (a repeated root); and if it is negative, there are no real solutions, only complex ones. Thus, a quadratic equation does not always have two solutions.
What do you do if you have a negative discriminant in a quadriatic equation?
By calculating the discriminant of the equation and if it's negative the equation will have no solutions
Could you ever have three solutions to a quadratic equation?
No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).
What is true about a quadratic if the discriminant is negative?
There are two complex solutions.
What is the type of the solution determined by?
It depends on the discriminant value of the quadratic equation. If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution; and if it is negative, there are two complex conjugate solutions.
What kind of solution does an equation has if the discriminant is negative?
If the discriminant is negaitve, there are no "real" solutions. The solutions are "imaginary".
If the discriminant is negative the equation has solutions?
As stated in the attached link, there are three possible discriminant conditions: Positive, Zero, or Negative. If the discriminant is negative, there are no real solutions but there are two imaginary solutions. So, yes there are solutions if the discriminant is negative. The solutions are imaginary, which is perfectly acceptable as solutions.
Explain how the number of solutions for a quadratic equation relates to the graph of the function?
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
What happens when there is negative under the square root in a quadratic equation?
When there is a negative number under the square root in a quadratic equation, it indicates that the equation has no real solutions. Instead, it results in complex or imaginary solutions, as the square root of a negative number involves the imaginary unit (i). This situation occurs when the discriminant (the part under the square root in the quadratic formula) is negative. Consequently, the quadratic graph does not intersect the x-axis, indicating no real roots.
What does the discriminant tell you?
The discriminant tells you how many solutions there are to an equation The discriminant is b2-4ac For example, two solutions for a equation would mean the discriminant is positive. If it had 1 solution would mean the discriminant is zero If it had no solutions would mean that the discriminant is negative
