Finding Value of Variable for an Equation that Touches a Curve

[fiejee]

Hello, I'm familiar on how to complete this type of question when the result is a quadratic, but how do I solve it for a solution with multiple 'a', 'b' and 'c' values??



Answer is + or - the root of 65

Thanks.

 

[Quaid]

Hello fiejee:

You're given an expression for symbol y.

y = 2x + k

Replace symbol y in the second equation with (2x+k) and simplify by multiplying out everything and combining like-terms.

You will end up with a quadratic equation.

Set the discriminant of this quadratic equation equal to zero, and then solve for k.

Cheers

 

[fiejee]

hello, yes I did that, but the problem I was having was that I end up with 2 sets of squared values. What do I do with it? How do I solve it as a quadratic?

I end up with: 13x² +2k² +10xk -5

 

[Deleted member 4993]

hello, yes I did that, but the problem I was having was that I end up with 2 sets of squared values. What do I do with it? How do I solve it as a quadratic?

I end up with: 13x² +2k² +10xk -5

Great .. set that equal to zero...

13x² +2k² +10xk -5 = 0

calculate the discriminant (D) using a = 13, b = 10k and c = 2k² -5

set D = 0 and solve for "k"

 

[fiejee]

I see, so any extra variables, I just tag together with 'C'

It works! I guess this math stuff does work. Thank you

 

[Quaid]

so any extra variables, I just tag together with 'C'

Not variables! Only constants (including parameters).

That is, when variable values are combined with constant values, the resulting expression is no longer a constant.

An expression represents a constant only when all of its symbols represent constants (including parameters).

Cheers