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If a quadratic function is 0 for any value of the variable, then that value is a solution.

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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: Are there no real solutions if a quadratic function is 0?
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If the discriminant of a quadratic equation is -4 how many solutions does the equation have?

If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.

How can you have one solution in something that is quadratic?

b^2 - 4ac, the discriminant will tell you that a quadratic equation may have one real solution( discriminant = 0 ) , two real solutions( discriminant > 0 ), or no real solutions( discriminant < 0 ).

How many real solutions does the following quadratic equation have by using the discriminant?

If the discriminant > 0 then 2 distinct real solutions.If the discriminant = 0 then 1 double real solution.If the discriminant < 0 then no real solutions (though there are two complex solutions).

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.

When is there no real solutions for a quadratic equation?

It's when ax2+bx+c=0 if b2-4ac= is negative

Why quadratic equations have two solutions?

If the discriminant of b2-4ac of the quadratic equation is greater the 0 then it will have 2 solutions.

What is the discriminant to determine how many real number solutions the quadratic equation -4j2 plus 3j-28 equals 0 has?

The discriminant is -439 and so there are no real solutions.

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 &Acirc;&plusmn; sqrt(d)]/(2a). Since D = 0, the both solutions are equal to -b/(2a), a single real solution.

What is x2 -2x plus 2 equals 0?

It is a quadratic equation with no real roots or real solutions. In the complex domain, the solutions are 1 +/- i where i is the imaginary square root of -1.

How many real solutions are there for the equation x2 plus 3x plus 5 equals 0?

There are no real solutions because the discriminant of the quadratic equation is less than zero.

What statement must be true of an equation before you can use the quadratic formula to find the solutions?

The quadratic formula can be used to find the solutions of a quadratic equation - not a linear or cubic, or non-polynomial equation. The quadratic formula will always provide the solutions to a quadratic equation - whether the solutions are rational, real or complex numbers.

Can there be a real and imaginary solution to a quadratic equation?

Yes, there can be a pure imaginary imaginary solution, as i2 =-1 and -i2 = 1. Or there can be a pure real solution or there can be a complex solution.For a quadratic equation ax2+ bx + c = 0, it depends on the value of the discriminant [b2 - 4ac], which is the value inside the radical of the quadratic formula.[b2 - 4ac] > 0 : Two distinct real solutions.[b2 - 4ac] = 0 : Two equal real solutions (double root).[b2 - 4ac] < 0 : Two complex solutions; they will be pure imaginary if b = 0, they will have both real and imaginary parts if b is nonzero.

How can you tell how many solutions a quadratic equation will have without solving it?

A quadratic equation can have a maximum of 2 solutions. If the discriminant (b2-4ac) turns out to be less than 0, the equation will have no real roots. If the Discriminant is equal to 0, it will have equal roots. But, if the discriminant turns out to be more than 0,then the equation will have unequal and real roots.

Do all linear quadratic systems have two solutions or one?

They will have 2 different solutions or 2 equal solutions and some times none depending on the value of the discriminant within the quadratic equation

What is the quadratic equation with solutions of 7i?

x2 + 49 = 0

What determine how many solutions a quadratic equation will have and whether they are real or imaginary?

The quadratic equation is: Ax2+ Bx + C = 0-- The equation always has two solutions. They arex = 1/2A [ - B + sqrt(B2 - 4AC) ]x = 1/2A [ - B - sqrt(B2 - 4AC) ] .-- The solutions are real if ( B2 > or = 4AC ).-- The solutions are equal if ( B2 = 4AC ).-- The solutions are complex conjugates if ( B2 < 4AC ).-- The solutions are pure imaginary if ( B = 0 ) & (4AC>0 i.e. -4AC

What are the domain and range of the quadratic parent function?

The domain is all real numbers, and the range is nonnegative real numbers (y &ge; 0).

How many solutions does a quadratic equation have when it is expressed in the form of ax2 plus bx plus c0 where a does not 0?

Assuming a, b, and c are real numbers, there are three possibilities for the solutions, depending on whether the discriminant - the square root part in the quadratic formula - is positive, zero, or negative:Two real solutionsOne ("double") real solutionTwo complex solutions

How do you know if a quadratic equation will have more than one solutions?

Write the quadratic equation in the standard form: ax2 + bx + c = 0 Then calculate the discriminant = b2 - 4ac If the discriminant is greater than zero, there are two distinct real solutions. If the discriminant is zero, there is one real solution. If the discriminany is less than zero, there are no real solutions (there will be two distinct imaginary solutions).

Can a system of two quadratic equations have two solutions?

Yes. It can have 0, 1, or 2 solutions.

How many and what type of solutions does the quadratic function x2 -10x plus 25 equals 0 have?

You are supposed to calculate the so-called discriminant, b2 - 4ac. If the result is positive, the equation has two real solutions; if it is zero, one real solution; if it is negative, no real solution (and two complex solutions). For this particular equation, a = 1, b = -10, and c = 25.

How do you recognize when an equation has no real solution or an infinite number of solutions?

It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.

Use the discriminant to determine how many real number solutions the quadratic equation -4j to the second power plus 3j - 28 equals 0 has?

It has no real roots.

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 x&sup2; + 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: Ax&sup2; + Bx + C = 0. The term [B&sup2; - 4AC] will determine if the solution is a double-root, or if the answer is real or complex.if B&sup2; = 4AC, then a double-root (real).if B&sup2; > 4AC, then 2 real rootsif B&sup2; < 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 x&sup2; + 4 = 0]Example of 2 real and opposite sign: x&sup2; - 4 = 0; 2 and -2 are solutions.

What is the difference between a real number and a no solution answer?

For solving a quadratic, you mean? Well, if you have real solutions you know that your quadratic has real numbers that make f(x) equal 0. For example, the quadratic f(x) = x^2 - x - 6 has -2 and 3 for solutions, because if you put in either of those two numbers for x, you get 0.I don't know how far along in your math career you are, but there aren't really any quadratics with no solutions, just with no real solutions. Some quadratics require you to take the square root of a negative number to get a solution, which is acceptable, it's just not a real solution anymore.