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27 May 2020, 04:50
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Difficulty:
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64% (01:46) correct
36%
(01:51)
wrong
based on 310
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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
Are You Up For the Challenge: 700 Level Questions
A. 22
B. 23
C. 24
D. 25
E. 26
Are You Up For the Challenge: 700 Level Questions
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
A. 22
B. 23
C. 24
D. 25
E. 26
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 \(b^2 > 4*a*c ….. Eq.(iii)\)
- o \(a = 1, b = 10\) and \(c = n\)
o So, for two distinct real roots, \(10^2 > 4*1*n\)
- \(⟹100 > 4n ⟹n < 25\)
General Discussion
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)
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)
