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If f1(x) = x2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots is
Correct answer is '24'. Can you explain this answer?
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If f1(x) = x2 + 11x + n and f2(x) = x, then the largest positive integ...
f1(x) = x2 + 11x + n and f2(x) = x,
f1(x) = f2(x)
x2 + 11x + n = x
x2 + 10x + n = 0
For this equation to have distinct real roots, b2 - 4ac>0
102> 4n
=> n < 100/4
=> n < 25
Thus, largest integral value that n can take is 24.
Positive Mark: 3
Negative Mark: 0
Most Upvoted Answer
If f1(x) = x2 + 11x + n and f2(x) = x, then the largest positive integ...
Problem Analysis:
We are given two functions f1(x) and f2(x) and we need to find the largest positive integer n such that the equation f1(x) = f2(x) has two distinct real roots.
Given:
f1(x) = x^2 + 11x + n
f2(x) = x
Approach:
To find the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, we need to solve the equation and analyze the discriminant.
Solving the Equation:
Setting f1(x) equal to f2(x), we have:
x^2 + 11x + n = x
Simplifying the equation, we get:
x^2 + 10x + n = 0
Analyzing the Discriminant:
For the equation ax^2 + bx + c = 0, the discriminant is given by Δ = b^2 - 4ac. If Δ > 0, the equation has two distinct real roots.
In our equation, a = 1, b = 10, and c = n. Therefore, the discriminant is:
Δ = (10)^2 - 4(1)(n) = 100 - 4n
Since we want Δ > 0, we have:
100 - 4n > 0
4n < />
n < />
Therefore, the largest possible value for n is 24.
Conclusion:
The largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots is 24.
We are given two functions f1(x) and f2(x) and we need to find the largest positive integer n such that the equation f1(x) = f2(x) has two distinct real roots.
Given:
f1(x) = x^2 + 11x + n
f2(x) = x
Approach:
To find the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, we need to solve the equation and analyze the discriminant.
Solving the Equation:
Setting f1(x) equal to f2(x), we have:
x^2 + 11x + n = x
Simplifying the equation, we get:
x^2 + 10x + n = 0
Analyzing the Discriminant:
For the equation ax^2 + bx + c = 0, the discriminant is given by Δ = b^2 - 4ac. If Δ > 0, the equation has two distinct real roots.
In our equation, a = 1, b = 10, and c = n. Therefore, the discriminant is:
Δ = (10)^2 - 4(1)(n) = 100 - 4n
Since we want Δ > 0, we have:
100 - 4n > 0
4n < />
n < />
Therefore, the largest possible value for n is 24.
Conclusion:
The largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots is 24.
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If f1(x) = x2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots isCorrect answer is '24'. Can you explain this answer?
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