Is it possible for a quadratic equation to have one or more solutions even when the quadratic expression Cannot be factored?

Yes, only certain quadratic equations are factorable. All the rest that can’t be factored? You’ll have to resort to another method to solve those. – if there’s a factor pair that you can add or subtract together to equal the b coefficient, then the equation is factorable.

Can an inequality have more than one solution?

Most of the time, an inequality has more than one or even infinity solutions. For example the inequality: x>3 . There’s an infinite amount of these numbers (e.g. 4, 5, 100, 100000, 6541564564654645 …). The inequality has an infinite amount of solutions.

Can an equation have more than one answer?

There can be more than one solution to a system of equations. A system of linear equations will have one point of intersection, or one solution. To graph a system of equations that are written in standard form, you must rewrite the equations in slope -intercept form.

How do you tell if an equation Cannot be factored?

The most reliable way I can think of to find out if a polynomial is factorable or not is to plug it into your calculator, and find your zeroes. If those zeroes are weird long decimals (or don’t exist), then you probably can’t factor it. Then, you’d have to use the quadratic formula.

Does every quadratic equation have two solutions?

Every quadratic equation has two solutions and can be factorized, but as level of difficulty rises, splitting may not be easy and one may tend to use quadratic formula.

How many possible solutions does an inequality have?

The solution set of an inequality is the set of all solutions. Typically an inequality has infinitely many solutions and the solution set is easily described using interval notation. The solution set of example 1 is the set of all x <= 7.

Can mathematics be ambiguous?

Abstract: even in mathematics, ambiguities can be hard to spot. The phenomenon seen here in arithmetic goes beyond the usual PEMDAS rule and illustrates an ambiguity which can lead to heated arguments and discussions.

What makes an equation have infinite solutions?

If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.

What do you do when an equation Cannot be factored?

When asked to solve a quadratic equation that you just can’t seem to factor (or that just doesn’t factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form.

What happens when you cant factor a polynomial?

So, if you can’t factor the polynomial then you won’t be able to even start the problem let alone finish it. A common method of factoring numbers is to completely factor the number into positive prime factors. A prime number is a number whose only positive factors are 1 and itself.

What are the factors of an equation?

The factors of any equation can be an integer, a variable or an algebraic expression itself. To the factor, a number means to break it up into numbers that can be multiplied to get the original number. For example, Also, numbers can be factorized into different combinations.

What happens if you can’t factor a polynomial?

There are many sections in later chapters where the first step will be to factor a polynomial. So, if you can’t factor the polynomial then you won’t be able to even start the problem let alone finish it. Let’s start out by talking a little bit about just what factoring is.

What is the formula for factoring a quadratic equation?

Factorization Formula for a Quadratic Polynomial A “quadratic” is a polynomial that is written like “ax 2 + bx + c”, where “a”, “b”, and “c” are just numbers. For an easy case of factoring, you can identify the two numbers that will not only multiply to equal the constant term “c” but also add up to equal “b,” the coefficient on the x-term.

What is the factorisation method in Algebra?

In the factorisation method, we reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable or an algebraic expression itself.