If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po

Question

If  \sqrt{k}  and  -\sqrt{k}  are the solutions to x^4 - 10x^2 + 25 = 0, where k is a positive constant, then k =

A. 0
B. 1
C. 3
D. 5
E. 10

saswata4s · Answer

Solutions of x^4 - 10x^2 + 25 = 0 are √k and - √k;

So we can say x = √k and x = - √k and x^2 = k;

Now, 
x^4 - 10x^2 + 25 = 0
=> (x^2 -5)^2 = 0
=> x^2 -5 = 0
=> x^2 = 5
=> k = 5; Hence, ans D.

Cheers.

BrentGMATPrepNow · Answer

Let's first solve the equation x⁴ - 10x² + 25 = 0
Factor to get: (x² - 5)(x² - 5) = 0
So, it must be the case that x² - 5 = 0
Take x² - 5 = 0 and add 5 to both sides to get: x² = 5

So, x = √5 or x = -√5
We're told that the solutions are √k and -√k
This means that k = 5

Answer: D

Cheers,
Brent

JeffTargetTestPrep · Answer

Let’s start by factoring x^4 - 10x^2 + 25 = 0:

(x^2 - 5)(x^2 - 5) = 0

Thus:

x^2 - 5 = 0

x^2 = 5

x = √5 or x = -√5, and thus k = 5.

Answer: D

Abhishek009 · Answer

\sqrt{k}=x

So,  x^4 = k^2  &  x^2 = k

So,  k^2 -10k + 25 = 0

Solve it  k = 5 , Answer must be (D)

WizakoMani · Answer

√k and -√k are the solutions mean that x = √k and -√k.
Squaring on both sides
 x^2 = k  --------(i)

Factorising the given equation, we get  (x^2 - 5)(x^2 - 5)= 0  and  (x^2 - 5)^2= 0 .

(x² - 5) = 0 --> x² = 5. comparing it with (i), k = 5

Option D.

If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po

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GMAT Problem Solving (PS) Questions

If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards