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Bunuel
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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the la 27 May 2020, 04:50
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

Question Stats:

64% (01:46) correct 36% (01:49) wrong based on 361 sessions

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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the largest positive integer n for which f(x) = g(x) has two distinct real roots?

A. 22
B. 23
C. 24
D. 25
E. 26


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C
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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the la 27 May 2020, 06:12
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Bunuel
If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the largest positive integer n for which f(x) = g(x) has two distinct real roots?

A. 22
B. 23
C. 24
D. 25
E. 26
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Solution


    • \(f(x) = x^2 + 11x + n\)
    • \(g(x) = x\)
    • So, \(f(x) = g(x) ⟹ x^2 + 11x + n = x ⟹ x^2 + 10x + n = 0 ……….Eq.(i)\)
    • Therefore, we need to find the largest positive integral value of n for which Eq.(i) will have two real and distinct roots.
    • The standard quadratic equation \(ax^2 + bx + c = 0 ……Eq.(ii)\)
      o Will have two real and distinct roots, if \(b^2 > 4*a*c ….. Eq.(iii)\)
    • Now, comparing Eq.(i) and Eq.(ii), we get,
      o \(a = 1, b = 10\) and \(c = n\)
      o So, for two distinct real roots, \(10^2 > 4*1*n\)
        \(⟹100 > 4n ⟹n < 25\)
    • Therefore, largest positive integral value of \(n = 24\)
Thus, the correct answer is Option C.
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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the la 27 May 2020, 06:08
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Equating f(x) =g(x)
we get,
x^2+10x+n=0
therefore,
x = -5 + (sqrt(100-4n)/2)
or x = -5 - (sqrt(100-4n)/2)

For x to be distinct and real, maximum number n can be is 24.
Answer Choice (C)
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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the la 27 May 2020, 07:26
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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the largest positive integer n for which f(x) = g(x) has two distinct real roots?

A. 22
B. 23
C. 24--> correct: f(x) = g(x) => x^2 + 11x + n =x => x^2 + 10x + n =0 =>(x-5)^2 = 5^2-n, because x has two distinct real roots, (x-5)^2 = 5^2-n > 0 => n<5^2 => n<25, so largest positive integer n = 24
D. 25
E. 26
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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the la 27 May 2020, 10:37
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See the attachment. C
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1.PNG
1.PNG [ 20.97 KiB | Viewed 4903 times ]

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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the la 31 May 2020, 11:23
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Bunuel
If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the largest positive integer n for which f(x) = g(x) has two distinct real roots?

A. 22
B. 23
C. 24
D. 25
E. 26


Show more
Solution:

Setting f(x) = g(x), we have:

x^2 + 11x + n = x

x^2 + 10x + n = 0

In order to have two distinct real roots, the discriminant b^2 - 4ac must be greater than 0. Therefore, we can create the inequality:

10^2 - 4(1)(n) > 0

100 - 4n > 0

100 > 4n

25 > n

Therefore, the largest positive integer value for n is 24.

Answer: C
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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the la 10 Jun 2020, 22:44
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Not sure how correct is my approach, but it didn't take more than 15 seconds.

n's largest value and 2 distinct integers.

Started to plug answer in the original equation. Only factors of 24 (8 and 3) makes the sum = 11. Hence, answer is C.
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If f(x) = x^2 + 11x + n and g(x) = x, then what is the value of the la 26 Apr 2025, 02:40
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