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Why do quadratic equations where the discriminant is 0 have exactly 1 real solution?
Suppose the quadratic equation is
ax^2 + bx + c = 0 and D = b^2 - 4ac is the discriminant.
Then the solutions to the quadratic equation are [-b ± sqrt(d)]/(2a).
Since D = 0, the both solutions are equal to -b/(2a), a single real solution.
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Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
How many times will the graph of a quadratic function cross or touch the x-axis if the discriminant is zero?
It will touch it at exactly 1 point. If a quadratic function is given as f(x) = ax2 + bx + c, let the discriminant be denoted as D. Then the graph of y = f(x) will cross the x-axis at the x-values x = (-b + sqrt(D))/(2a) and x = (-b - sqrt(D))/(2a). When the discriminant D = 0, these 2 x-values are actually the same. Thus the graph will touch the x-axis only once.
Why is it necessary to check for extraneous solutions in radical equations?
1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
A quadratic polynomial has a degree greater than 2?
true :) apex! * * * * * APEX gets it wrong - again! A quadratic polynomial has degree 2. Not greater than, nor less than but exactly equal to 2.
Use the substitution method to solve the system of equations. Choose the correct ordered pair. 2y plus 2x 20 y - 2x 4?
It is not possible to know exactly what the question is because the browser used by this site is almost totally useless for mathematical questions: it rejects most symbols. If the equations are 2y + 2x = 20 and y - 2x = 4,then the solution is (2, 8).
If the discriminant of an equation is zero then?
The term "discriminant" is usually used for quadratic equations. If the discriminant is zero, then the equation has exactly one solution.
Why are there usually two solutions to a quadratic equation?
In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.
A system of equations with exactly one solution?
A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.
A system of two linear equations has exactly one solution if?
The slopes (gradients) of the two equations are different.
If a system of equations is independent how many soultions will it have?
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
How to tell if there are no real roots?
The real roots of what, exactly? If you mean a square trinomial, then: If the discriminant is positive, the polynomial has two real roots. If the discriminant is zero, the polynomial has one (double) real root. If the discriminant is negative, the polynomial has two complex roots (and of course no real roots). The discriminant is the term under the square root in the quadratic equation, in other words, b2 - 4ac.
How do you know how many solutions a quadratic equation will have?
A quadratic equation has the formAx2 + Bx + C = 0,where A, B, and C are numbers and x is a variable. Since the polynomial here has degree 2 (the highest exponent of x), it either has 0, 1, 2, or infinitely many solutions.The infinitely many solutions only happens when A, B, and C are all equal to zero. Otherwise, we can find the number of solutions by examining the discriminant, which in this case is the quantity B2 - 4AC. If the discriminant is negative, there are no (real) solutions. If the discriminant equals zero, we have what is called a "repeated root" and there is exactly one (real) solution. Otherwise, if the discriminant is positive, there are two distinct (real) solutions.
Does a quadratic equation has exactly one solution?
Normally it has two solutions but sometimes the solutions can be the same.
If a system of linear equations has exactly one solution then the two lines are what?
perpendicular
What system of two linear equations in two variables that has exactly one solution?
An independent system has one solution.
What do you call the graphs that intersect at exactly one point which gives solution of the system?
They are straight line graphs that work out the solutions of 2 equations or simultaneous equations
