CA Foundation Exam > CA Foundation Questions > If x3 - 6x2 + 11x-6 = 0 then find the value o...
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If x3 - 6x2 + 11x-6 = 0 then find the value of (3x-4).
- a)(1, 2, 3)
- b)(-1, 2, 5)
- c)(-1, 3, 5)
- d)(2, 3, 5)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If x3 - 6x2 + 11x-6 = 0 then find the value of (3x-4).a)(1, 2, 3)b)(-1...
Let p(x) = x3 - 6x2 + 11x - 6
By trial, we find that
p(1) = (1)3 - 6(1)2 + 11(1) - 6 = 0
∴ By converse of factor theorem, (x - 1) is a factor of p(x).
Now, x3 - 6x2 + 11x - 6
= x2 (x - 1)- 5x (x - 1) + 6 (x - 1)
= (x - 1) (x2 - 5x + 6)
= (x - 1) {x2 - 2x - 3x + 6}
= (x - 1) {x(x - 2)-3 (x - 2)}
= (x - 1)(x - 2)(x - 3)
By trial, we find that
p(1) = (1)3 - 6(1)2 + 11(1) - 6 = 0
∴ By converse of factor theorem, (x - 1) is a factor of p(x).
Now, x3 - 6x2 + 11x - 6
= x2 (x - 1)- 5x (x - 1) + 6 (x - 1)
= (x - 1) (x2 - 5x + 6)
= (x - 1) {x2 - 2x - 3x + 6}
= (x - 1) {x(x - 2)-3 (x - 2)}
= (x - 1)(x - 2)(x - 3)
This question is part of UPSC exam. View all CA Foundation courses
Most Upvoted Answer
If x3 - 6x2 + 11x-6 = 0 then find the value of (3x-4).a)(1, 2, 3)b)(-1...
Solution:
Given equation is x3 - 6x2 + 11x - 6 = 0
We need to find the value of (3x - 4)
Let's factorize the given equation
x3 - 6x2 + 11x - 6 = 0
x3 - 3x2 - 3x2 + 9x + 2x - 6 = 0
(x - 3) (x2 - 3x + 2) + (2x - 6) = 0
(x - 3) (x - 1) (x - 2) + 2(x - 3) = 0
(x - 3) (x2 - 3x + 2) = 0
x = 3, 1, 2
Now, we need to find the value of (3x - 4) for each of these values of x.
a) (3x - 4) when x = 1
(3x - 4) = (3(1) - 4) = -1
b) (3x - 4) when x = 2
(3x - 4) = (3(2) - 4) = 2
c) (3x - 4) when x = 3
(3x - 4) = (3(3) - 4) = 5
Therefore, the values of (3x - 4) for the given values of x are:
a) -1
b) 2
c) 5
Option B (-1, 2, 5) is the correct answer.
Given equation is x3 - 6x2 + 11x - 6 = 0
We need to find the value of (3x - 4)
Let's factorize the given equation
x3 - 6x2 + 11x - 6 = 0
x3 - 3x2 - 3x2 + 9x + 2x - 6 = 0
(x - 3) (x2 - 3x + 2) + (2x - 6) = 0
(x - 3) (x - 1) (x - 2) + 2(x - 3) = 0
(x - 3) (x2 - 3x + 2) = 0
x = 3, 1, 2
Now, we need to find the value of (3x - 4) for each of these values of x.
a) (3x - 4) when x = 1
(3x - 4) = (3(1) - 4) = -1
b) (3x - 4) when x = 2
(3x - 4) = (3(2) - 4) = 2
c) (3x - 4) when x = 3
(3x - 4) = (3(3) - 4) = 5
Therefore, the values of (3x - 4) for the given values of x are:
a) -1
b) 2
c) 5
Option B (-1, 2, 5) is the correct answer.
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If x3 - 6x2 + 11x-6 = 0 then find the value of (3x-4).a)(1, 2, 3)b)(-1, 2, 5)c)(-1, 3, 5)d)(2, 3, 5)Correct answer is option 'B'. Can you explain this answer?
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