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If the discriminant of a quadratic equation is less than zero what is true about it?
If the discriminant of a quadratic equation is less than zero, it indicates that the equation has no real solutions. Instead, it has two complex (or imaginary) solutions that are conjugates of each other. This means the parabola represented by the quadratic equation does not intersect the x-axis.
Why is a quadratic function better than other functions?
A quadratic function is often preferred for modeling certain types of real-world phenomena due to its parabolic shape, which can represent a variety of relationships, such as projectile motion or profit maximization. Its mathematical properties, including the ability to easily find the vertex and solutions via factoring or the quadratic formula, make it versatile and manageable. Additionally, quadratic functions can capture relationships that exhibit acceleration or deceleration, which linear functions cannot. This makes them particularly useful in fields like physics, economics, and engineering.
What are the solutions for x when y equals 0 in the quadratic function y equals x2 plus x?
y = x2 + x = 0 x (X + 1) = 0 x = 0 is one solution x = -1 is the other
When are these kinds of numbers solutions to quadratic equations?
You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
How many complex number solutions can exist for a quadratic equation?
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.
What are 3 other names for solutions of a quadratic equation?
Roots, zeroes, and x values are 3 other names for solutions of a quadratic equation.
What are other names for solutions of a quadratic?
They are the roots or zeros. They are also the x-intercepts if they are real numbers.
How many solution will there be if the quadratic equation does not touch or cross the x-axis?
0 real solutions. There are other solutions in the complex planes (with i, the imaginary number), but there are no real solutions.
If the discriminant of a quadratic equation is less than zero what is true about it?
If the discriminant of a quadratic equation is less than zero, it indicates that the equation has no real solutions. Instead, it has two complex (or imaginary) solutions that are conjugates of each other. This means the parabola represented by the quadratic equation does not intersect the x-axis.
What is the average of the two soultions for the quadratic equation?
Replace the discriminant (the root) in the quadratic formula with zero - that will give you the average. In other words: (average of solutions) = -b/2a.
What is a zero of a quadratic function?
The "zero" or "root" of such a function - or of any other function - is the answer to the question: "What value must the variable 'x' have, to let the function have a value of zero?" Or any other variable, depending how the function is defined.
Other names for input of a function?
other names for the input of a function are: 1. x 2. domain
Why is a quadratic function better than other functions?
A quadratic function is often preferred for modeling certain types of real-world phenomena due to its parabolic shape, which can represent a variety of relationships, such as projectile motion or profit maximization. Its mathematical properties, including the ability to easily find the vertex and solutions via factoring or the quadratic formula, make it versatile and manageable. Additionally, quadratic functions can capture relationships that exhibit acceleration or deceleration, which linear functions cannot. This makes them particularly useful in fields like physics, economics, and engineering.
What are the solutions for x when y equals 0 in the quadratic function y equals x2 plus x?
y = x2 + x = 0 x (X + 1) = 0 x = 0 is one solution x = -1 is the other
What is the quadratic formula used for?
The quadratic formula is used all the time to solve quadratic equations, often when the factors are fractions or decimals but sometimes as the first choice of solving method. The quadratic formula is sometimes faster than completing the square or any other factoring methods. Quadratic formula find: -x-intercept -where the parabola cross the x-axis -roots -solutions
What does it mean if the quadratic equation has no solution?
Generally, when we say a quadratic equation has no solutions, it means that the graph does not cross the x-axis at all.In other words, it means that there are no values for x when y equals 0 (because the line y=0 IS the x-axis.)Hope that helps.Jamz159
When are these kinds of numbers solutions to quadratic equations?
You need to be more specific. A quadratic equation will have 2 solutions. The 2 solutions can be equal (such as x² + 2x + 1 = 0, solution is -1 and -1). If one of the solutions is a real number, then the other solution will also be a real number. If one of the solutions is a complex number, then the other solution will also be a complex number. [a complex number has a real component and an imaginary component]In the equation: Ax² + Bx + C = 0. The term [B² - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B² = 4AC, then a double-root (real).if B² > 4AC, then 2 real rootsif B² < 4AC, then the quadratic formula will produce a square root of a negative number, and the solution will be 2 complex numbers.If B = 0, then the numbers will be either pure imaginary or real, and negatives of each other [ example 2i and -2i are solutions to x² + 4 = 0]Example of 2 real and opposite sign: x² - 4 = 0; 2 and -2 are solutions.
