For What Values of K the Quadratic Equation (K + 1)x^2 – 2(K – 1)x + 1 GMAT Problem Solving

Question: For what values of K the quadratic equation (K + 1)x^2 – 2(K – 1)x + 1 = 0 has equal roots?

1. 0 or -1
2. 0 or 1
3. 0 or 2
4. 0 or 3
5. 0 or 4

Correct Answer: D

Solution and Explanation:

Approach Solution 1:
(K+1)x^2–2(K–1)x+1= 0
[−2(k−1)]^2= 4∗(k+1)∗1
i.e. 4k^2+4−8k= 4k+4
i.e. 4k^2= 12k
i.e. k = 3 or 0
 

Approach Solution 2:
4(K-1)^2 - 4(K+1)= 0
K^2 - 2K + 1 - K - 1= 0
K^2 - 3K= 0

K= 0 or 3

Approach Solution 3:
Since roots are equal.
Therefore d= 0…(1)
(k+1)x^2-2(k-1)x+1= 0
d= b^2-4ac
d= (-2(k-1))^2-4(k+1)(1)
D- (-2k+2)^2-4k-4
d= 4k^2+4-8k-4k-4
Since (a+b)^2= a^2+b^2+2ab
d= 4k^2-12k
From (1), d= 0

Therefore, equation will be
0= 4k^2-12k
4k^2= 12k
k^2= 12/4
k^2= 3k
k^2-3k= 0
k(k-3)= 0
k= 0 or k-3= 0
k= 3
Therefore, values of k are 0,3

“For what values of K the quadratic equation (K + 1)x^2 – 2(K – 1)x + 1”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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