Find all integers k so that the trinomial can be factored

Ответ:

NeedsMajorHelp

16.01.2022

Mathematics

The trinomial will come out to be
(2m+a)(m+b)

for some integers

and

.

We know that ab=-5

because the constant term is -5.

We also know that $2bm+am=km\rightarrow2b+a=k$

Possibilities:
1. $a=1,\ b=-5\rightarrow k=2b+a=-9$
2. $a=5,\ b=-1\rightarrow k=2b+a=3$
3. $a=-1,\ b=5\rightarrow k=2b+a=9$
4. $a=-5,\ b=1\rightarrow k=2b+a=-3$

So

can be 9, 3, -9, or -3.

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Ответ:

gl648809

22.01.2020

Mathematics

I'll assume the first vector to be (5,-1).

The vectors are not orthogonal

Step-by-step explanation:

Two vectors are orthogonal if the angle between them is 90°.

An easy test consists of calculating their dot product. If it results zero then the vectors are perpendicular or orthogonal.

Recall the dot product between two vectors x(a,b) and y(c,d) is:

$\vec x\cdot \vec y=|\vec x|.|\vec y|.cos\alpha$

Also:

$\vec x\cdot \vec y=a.c+b.d$

Where $\alpha$ is the angle between the vectors. If the angle is 90°, then cos 90° =0, and the dot product is 0.

Let's test if the vectors (5,-1) (4,32) are orthogonal:

$\vec x\cdot \vec y=5*4+(-1)*(32)=20-32=-12$

Since the dot product is not zero, the vectors are not orthogonal

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Find all integers k so that the trinomial can be factored 2m^2+km-5

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