Application of Quadratic Functions And Equations.. HELP!

T

teripaan

New member
Joined
Sep 21, 2008
Messages
4
Grade 11 math question..

Show that the equation 2x^2 - 5x + 2 = 0 has roots that are reciprocals of each other. Under what conditions will a quadratic equation in the form ax ^2 +bx + c = 0 have roots that are reciprocals of each other?
 
teripaan said:
Show that the equation 2x^2 - 5x + 2 = 0 has roots that are reciprocals of each other. Under what conditions will a quadratic equation in the form ax ^2 +bx + c = 0 have roots that are reciprocals of each other?
Click to expand...
What have you tried? How far have you gotten? Where are you stuck? For instance, you've applied the Quadratic Formula to the first quadratic and solved to get... what? And where did you go from there?

Please be complete. Thank you! :D

Eliz.
 
Never mind.. i got the answer to the question.. my friend helped me out..

thanks anyways!
 
2x² - 5x + 2 = 0
(2x - 1)(x - 2) = 0
x = ½ and x = 2

½ and 2 are roots that are reciprocals of each other.

Under what conditions will a quadratic equation in the form ax ² +bx + c = 0 have roots that are reciprocals of each other?

If the roots are reciprocals of each other a = c and |b| = the square of one root's numerator + the square of that root's denominator.

for ex.
2x² - 5x + 2 = 0
(x - 2)(2x - 1) = 0
x = 2 or x = ½
For 2x² - 5x + 2, a = c since both equal 2. |b| = 5 which looking at the root ½ is the numerator squared + the denominator squared, 1² + 2² = 1 + 4 = 5.

it looks right... is it?
 
teripaan said:
... Under what conditions will a quadratic equation in the form ax ² +bx + c = 0 have roots that are reciprocals of each other?

If the roots are reciprocals of each other a = c and |b| = the square of one root's numerator + the square of that root's denominator.

2x² - 5x + 2 = 0
(x - 2)(2x - 1) = 0
x = 2 or x = ½

a = c ... |b| = 5 ... is the numerator squared + the denominator squared, 1² + 2² = 5

it looks right... is it?
Click to expand...

Hello Teri:

Your friend is on the right track, but you need to fix one loophole.

Consider the zeros of polynomial x^2 + (17/4)x + 1

They are reciprocals, but 17/4 does not equal the sum of the squares of the numerator and denominator.

Here's a hint. Give the necessary conditions for reciprocal roots in terms of the values of b/a and c/a.

Cheers,

~ Mark :)

MY EDITS: added color and corrected spelling errors
 
I do not see why the second condition is at all necessary.

The necessary and sufficient condition is c = a (a < > 0)
 
Subhotosh Khan said:
I do not see why the second condition is at all necessary.
Click to expand...

It's not. Perhaps, in two more steps, the original poster would have come to that conclusion.

~ Mark :)
 
You must log in or register to reply here.
Top