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Anonymous Tue 15 Mar 17:44:50 2022 No.14306486 View Reply Original Report

Quoted By: >>14306500 >>14306534 >>14307591 >>14307606 >>14307778 >>14307851

how do i find the root of $(4x - 3)(2x + 5)$ ? I know it's a fraction but how do I convert it. Also what's this process called?
Is it $\frac{3}{4}, -\frac{5}{2}$ ?
Am I close?
Am retard btw

Anonymous

Anonymous Tue 15 Mar 2022 17:50:54 No.14306500 Report

Quoted By:

>>14306486
> Is it $\frac{3}{4}, -\frac{5}{2}$
Yes. x equal to either value makes the function zero hence they are roots.

Anonymous

Anonymous Tue 15 Mar 2022 18:05:11 No.14306534 Report

Quoted By:

>>14306486
>(4x?3)(2x+5)

Yes, go plot them this online. The two roots are where the y value is zero. Note if you set x = 0, the y value will be -15 which is also on the graph.

https://www.wolframalpha.com/input?i=plot+%284x?3%29%282x%2B5%29

Anonymous

Anonymous Wed 16 Mar 2022 01:40:37 No.14307591 Report

Quoted By:

>>14306486
Let's call this polynomial $p(x)$ . The roots of a polynomial are the values of $x$ that make it 0. So we're trying to solve the equation $p(x) = 0$ . Here, you factored the polynomial and got $p(x) = (4x - 3)(2x + 5)$ . Since we're trying to find values of $x$ which make this 0, we solve $(4x - 3)(2x + 5) = 0$ .

Well, notice how for any two real (or complex) numbers $a, b$ , the product $a \cdot b = 0$ only when *at least* one of the two numbers is 0. Our numbers are actually the expressions in the parantheses. So here, the equation $(4x - 3)(2x + 5) = 0$ is solved when either $(4x - 3) = 0$ or $(2x + 5) = 0$ . From here, we just isolate $x$ to get the fractions.

$4x - 3 = 0 \Rightarrow 4x = 3 \Rightarrow x = 3 / 4$
$2x + 5 = 0 \Rightarrow 2x = -5 \Rightarrow x = -5 / 2$

Anonymous

Anonymous Wed 16 Mar 2022 01:43:14 No.14307596 Report

Quoted By:

test

Anonymous

Anonymous Wed 16 Mar 2022 01:47:27 No.14307606 Report

Quoted By:

>>14306486
$(4x?3)(2x+5) =0$ when $4x-3 =0$ or $2x+5 =0$ .

In the first case add 3 to both sided
$4x=3$
then divide by four
$x = \frac{3}{4}$ .
It's similar in the second case.

>I know it's a fraction but how do I convert it.
What?
>Also what's this process called?
It's called algebra.

Anonymous

Anonymous Wed 16 Mar 2022 03:03:31 No.14307778 Report

Quoted By:

>>14306486
the thing that is tripping your up is that the function is already factored to reveal the roots, usually you will get ax^2+bx+c =0 form and be required to do actual work to find the roots.

Anonymous

Anonymous Wed 16 Mar 2022 03:38:37 No.14307851 Report

Quoted By:

>>14306486
By root, you mean where it is equal to 0? Where either product can be 0 for it to be satisfied? Where you take each product and set to 0 and solve for x?

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