Question

Two numbers have a sum of 9 and a product of 20.

What single-variable quadratic equation in the form ax^2 + bx + c = 0 can be used to represent the product of the two numbers?

Answer 1

Let's say that x is number 1.
The second number would be (9 - x)
Now, can you do it? =)

Answer 2

X + Y = 9
X * Y = 20

Answer 3

But it's written -SINGLE VARIABLE-

Answer 4

What does that mean\?

Answer 5

You cannot use two variables.

Answer 6

Weird

Answer 7

The two variables that you can use are x and (9 - x).

Answer 8

X - 9 uses 1 variable right

Answer 9

Yes.

Answer 10

We're using only one variable, i.e x.

Answer 11

X - 9 why does that work?

Answer 12

Because if one number is x, and the second number and x add up to 9, then we can use 9 - x, rite?

Answer 13

What about X - 9?

Answer 14

Okay, that wouldn't work. I know that the answer is 4 and 5. Take 4 as x. Would x - 9 work?

Answer 15

No

Answer 16

Exactly. So here's your answer.

Answer 17

Okay

Answer 18

@ParthKohli I do not know where to go from 9 - X

Answer 19

\(\Large \color{MidnightBlue}{\Rightarrow x + (9 - x) = 9 }\)
\(\Large \color{MidnightBlue}{\Rightarrow x + 9 - x = 9 }\)
\(\Large \color{MidnightBlue}{\Rightarrow 0 = 0 }\)
Agree?

Answer 20

yes

Answer 21

Then:

\(\Large \color{MidnightBlue}{\Rightarrow x * (9 - x) = 20 }\)
\(\Large \color{MidnightBlue}{\Rightarrow x * (9 - x) - 20 = 0 }\)
\(\Large \color{MidnightBlue}{\Rightarrow -x^2 +9x - 20= 0 }\)

And here is your quadratic equation.

Answer 22

@ParthKohli I lied ParthKohli when I said I agree'd

Answer 23

Lol

Answer 24

9 - x well x could resemble 4 right?

Answer 25

So 9 - 4 = 5 then 5 + 4 = 9 again right?|

Answer 26

Sure.

Answer 27

Is that the wrong way to think about it?

Answer 28

No, I guess

Answer 29

Okay so let's pretend x is 4 then

Answer 30

x∗(9−x)=20

well it's like 9 - 4 = 5, 5 * 4 = 20

Answer 31

Right?