Why does a quadratic function have 2 solutions?

There are usually two solutions because quadratic equations form a parabola in Cartesian coordinates. In almost any case involving a function, the parabola will intercept the x-axis at two points. Those two points are the two x values that cause the function to be equal to zero.

When we solve a quadratic equation by factoring Why do we move all terms to one side having zero on the other?

In other words, if the product of two numbers or two expressions equals zero, then one of the numbers or one of the expressions must equal zero because zero multiplied by anything equals zero. Multiplying the factors expands the equation to a string of terms separated by plus or minus signs.

Why is it necessary to set a quadratic equal to zero when solving by factoring?

The roots are the points where y = 0. You want to factor the equation to the form y = (x – a)(x – b). If you multiply two numbers and their product is 0, then one of the numbers must be 0. That is why we set the quadratic equal to 0.

Does a quadratic equation have two solutions?

A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real.

Why can’t a quadratic equation have more than two solutions?

Proof: Let us assumed that α, β and γ be three distinct roots of the quadratic equation of the general form ax2 + bx + c = 0, where a, b, c are three real numbers and a ≠ 0. Then, each one of α, β and γ will satisfy the given equation ax2 + bx + c = 0. Hence, every quadratic equation cannot have more than 2 roots.

Why does a quadratic equation with a positive discriminant have two real solutions?

If the discriminant is positive, this means that you have a positive number under the square root in the quadratic formula. This means you will end up with 2 real solutions. You can always take the square root of a positive number. If there are 2 real solutions, this also means that the graph will have 2 x-intercepts.

How do you identify quadratic equation that can be solved by factoring?

Therefore, when solving quadratic equations by factoring, we must always have the equation in the form “(quadratic expression) equals (zero)” before we make any attempt to solve the quadratic equation by factoring. Note that “x = 3, 4” means the same thing as “x = 3 or x = 4”; the only difference is the formatting.

Why are some equations equal to zero?

Essentially, the zero is stating where the equation intersects with the x axis, because when y = 0, the the equation is on the x axis. Also, it makes it really convenient for equations like y=8×2−16x−8 because when finding the root (or solution) (or value of x when = 0), we can divide out the 8.

What does it mean when an equation equals 0?

The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation.

Why does an equation have two solutions?

A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solution.

Why does every quadratic equation have exactly two roots?

Every quadratic equation has exactly two roots. This is a consequence of the fundamental theorem of algebra. In simpler terms, a quadratic expression can always be expressed as a product of two linear expressions. Equating the quadratic expression to zero is equivalent to equating this product to zero. This will always give us two roots.

Why do quadratics usually have two answers?

There’s no kno Quadratics usually have two answers because they can be reduced to a square root, in a suitable sense, and there are typically two square roots of any given value (since is equivalent to , and there are two choices of which factor on the left to make zero). Which one is the correct answer?

How do you find the solution to a quadratic equation?

The solution (s) to a quadratic equation is the point (s) where the parabola crosses the x x -axis. Solutions are also referred to as x x -intercepts, zeros, and roots. Become a Study.com member to unlock this answer!

Why is the square root of 4 a quadratic function?

Because quadratic functions are functions with the highest degree of 2, this means it’s a term which is squared (ax^2+bx+c)When x is squared it will have a positive and a negative solution eg square root of 4 is either 2 or -2. When there is only one solution that is because 0 and -0 is the same thing, that’s why there’s only one solution.