blitzbabeiy
2022-01-23
Answered

How can I convert $a{x}^{2}+bx+c=0$ to a FOIL-style $(x+d)(x-e)=0$ equation?

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Nevaeh Jensen

Answered 2022-01-24
Author has **14** answers

Step 1

Theres

Theres

Rylee Marshall

Answered 2022-01-25
Author has **6** answers

Step 1

If a polynomial has a root r (imaginary or real), then you can pull out a factor of$x-r$ .

For example, to factor${x}^{2}+1$ , we first find the roots. You can use the quadratic equation for this in general, but it's easy to see in this example that the roots are i and -i. This means the polynomial ${x}^{2}+1$ factors as $(x-i)(x+i)$ .

Notice this polynomial has no real solutions. There is no amount of algebraic trickery you can do to get around that fact. Depending on your application, you will either have to accept the imaginary roots or regard the polynomial as having no (real) solutions.

If a polynomial has a root r (imaginary or real), then you can pull out a factor of

For example, to factor

Notice this polynomial has no real solutions. There is no amount of algebraic trickery you can do to get around that fact. Depending on your application, you will either have to accept the imaginary roots or regard the polynomial as having no (real) solutions.

RizerMix

Answered 2022-01-27
Author has **438** answers

Step 1$a{x}^{2}+bx+c=a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})$ If you plug a number n into a polynomial and get 0, then $(x-n)$ is a factor of that polynomial. So the two numbers that you can plug into a quadratic polynomial that mkae it add up to 0 correspond to the two factors. But you can't get real numbers if the solutions are not real numbers.

asked 2022-04-30

I have a quadratic equation, $b{x}^{2}+2ax+b=0$ , with $a>b>0$ . I can solve this as followings,

${x}_{+}=\frac{-a+\sqrt{{a}^{2}-{b}^{2}}}{b},{x}_{-}=\frac{-a-\sqrt{{a}^{2}-{b}^{2}}}{b},$

In my text book, an inequality equation,$x}_{\{+\}}^{2}<1<{x}_{\{-\}}^{2$ , is written with the solution, but I cannot derive the equation. If you can, please teach me the derivation.

In my text book, an inequality equation,

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(a)$\pm \sqrt[()]{b}i$

(b)$a\pm bi$

(a)

(b)

asked 2021-12-02

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for the parabola’s axis of symmetry. Use the parabola to identify the function's domain and range,

Use the graphing tool to graph the equation, Use the vertex and the y-intercept when drawing the graph.

Click to enlarge graph

The exis of symmetry is

(Type an equation. Simplify your answer)

The domain of f is

(Type your answer in interval notation.)

The range of f is

(Type your answer in interval notation.)

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How to generate factors given the b-value of the quadratics is the hypotenuse of a Pythagorean Triple?

Given two quadratics with integer coefficients,

$y={x}^{2}+bx+c$ and ${x}^{2}+bx-c$

Given two quadratics with integer coefficients,

asked 2021-08-20

Graph the following equations and explain why they are not graphs of functions of x. |x |+ | y | = 1