Quadratic Equation Help Required

Question

Hi Guys,

I came across the below problem in one of the online gmat test..I got stuck in the middle...any suggestions to solve the problem..??

The function f(x) is given by 2x^2 +bx+c, b and c having specific numerical values. On replacing x by a number 2 greater than itself, f(x) increases by 12. What is the value of x ?

F(x) = 2x^2 +bx+c ......(1)

let r1 and r2 be the roots of hte equation:

r1 +r2 = -b/2
r1r2 = c/2

on replacing x by a number 2 greater than itself, as per my understanding the equation would be:

f(x+2) = (2x^2 +bx+c )+ 12.... (2)

f(x+2) = f(x) +12

i'm stuck here..any siggestions pls?

Regards,
anu

fluke · Answer

2(x+2)^2+b(x+2)+c = 2x^2+bx+c

After solving;
 x = \frac{2+b}{4} . Maybe some mistake. Please verify.

anuu · Answer

The answer choices given in the online test are:

-2, 2, -1,1 and cannot be determined.

Can you pls explain the last line where you have equated the two equations..
i do understand that u have replaced x with x+2 in the equation 2x^2+bx+c

thus 2x^2+bx+c = 2 (x+2)^2 + b(x+2) +c

why are we equating the two equations ? and the increase in 12 is not accounted for? Can you pls explain the concept?

Regards,
Anu

fluke · Answer

Oh, I missed the "+12" part. It should be there.

2(x+2)^2+b(x+2)+c=2x^2+bx+c+12 
 2(x^2+4+4x)+bx+2b+c=2x^2+bx+c+12 
 2x^2+8+8x+bx+2b+c=2x^2+bx+c+12 
 8+8x+2b=12 
 8x+2b=4 
 4x+b=2 
 x=\frac{2-b}{4}

So, x is dependent on the value of "b" and thus cannot be determined.

If b=0; x=1/2; will satisfy the condition
If b=2; x=0; will satisfy the condition
If b=1002; x=(2-b)/4= (2-1002)/4=-250 will satisfy the condition.
Thus, there is no fixed value of x.

Please let me know if something is not clear.

itsnotover · Answer

I agree with Fluke. Value of x is dependent on b.

To get f(x+2), replace x by x+2 in whole equation. So, f(x+2) = 2 (x+2)^2 + b(x+2) +c
and then equate it to f(x) by adding 12. I got the same answer as above post.

retro · Answer

Not to nit-pick but merely to suggest that I would not do so if I faced the question: why do you even calculate the roots/their sums/their products? This is not a question asking you to eke out the roots of the QE. Is it? I thought it is a waste of time. Just be wary that not every appearance that appears quadriatic needs be solved..That is a learning for me too.

Regards
Rahul

anuu · Answer

@ Rahul,
I too agree there is no need to calculate the sum/product of the roots. In the first instance i saw the question, i just wrote down the sum/product of the roots (thinking it might be of some use as I proceed solving the QE...but there is no use for the roots)..and yes in the real GMAT , it wud be waste of time doing this considering that there is only 2min for each question.

Anu

amit2k9 · Answer

x = (2-b)/4.

X will be in terms of b here.

Quadratic Equation Help Required

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