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If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?
- a)X3 + 4X2 – 32X
- b)X2 + 18X + 80
- c)X2 – 12X + 20
- d)X2 + 5X – 14
- e)X2 + 10X + 16
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
If X is a root of the equation a3 +8a2 – 20a, than which of the ...
The best answer is E.
The original equation is a3 +8a2 – 20a, it can be written as a(a – 2)(X + 10). The roots are 2,0 and (-10).
We are looking for an equation that has none of the same roots.
Answer E: X2 – 10X +16 = (X + 2)(X + 8) à This equation has none of the original roots. All the other answers have one or more of the same original roots.
We are looking for an equation that has none of the same roots.
Answer E: X2 – 10X +16 = (X + 2)(X + 8) à This equation has none of the original roots. All the other answers have one or more of the same original roots.
Most Upvoted Answer
If X is a root of the equation a3 +8a2 – 20a, than which of the ...
Explanation:
Given: X is a root of the equation a^3 + 8a^2 - 20a
Key Point: If X is a root of an equation, then substituting X into the equation should yield 0.
Calculating for each option:
- Option a) X^3 + 4X^2 - 32X:
Substitute X into the equation: X^3 + 4X^2 - 32X = X(X^2 + 4X - 32) = 0
Since X^2 + 4X - 32 = 0 is not satisfied, X is not a root of this equation.
- Option b) X^2 + 18X + 80:
Substitute X into the equation: X^2 + 18X + 80 = 0
Since X is a root of a cubic equation, it does not guarantee that X will be a root of a quadratic equation.
- Option c) X^2 - 12X + 20:
Substitute X into the equation: X^2 - 12X + 20 = 0
Since X is a root of a cubic equation, it does not guarantee that X will be a root of a quadratic equation.
- Option d) X^2 + 5X - 14:
Substitute X into the equation: X^2 + 5X - 14 = 0
Since X is a root of a cubic equation, it does not guarantee that X will be a root of a quadratic equation.
- Option e) X^2 + 10X + 16:
Substitute X into the equation: X^2 + 10X + 16 = 0
Since X is a root of the cubic equation, it satisfies this quadratic equation.
Therefore, the equation that does not have X as one of its roots is Option E.
Given: X is a root of the equation a^3 + 8a^2 - 20a
Key Point: If X is a root of an equation, then substituting X into the equation should yield 0.
Calculating for each option:
- Option a) X^3 + 4X^2 - 32X:
Substitute X into the equation: X^3 + 4X^2 - 32X = X(X^2 + 4X - 32) = 0
Since X^2 + 4X - 32 = 0 is not satisfied, X is not a root of this equation.
- Option b) X^2 + 18X + 80:
Substitute X into the equation: X^2 + 18X + 80 = 0
Since X is a root of a cubic equation, it does not guarantee that X will be a root of a quadratic equation.
- Option c) X^2 - 12X + 20:
Substitute X into the equation: X^2 - 12X + 20 = 0
Since X is a root of a cubic equation, it does not guarantee that X will be a root of a quadratic equation.
- Option d) X^2 + 5X - 14:
Substitute X into the equation: X^2 + 5X - 14 = 0
Since X is a root of a cubic equation, it does not guarantee that X will be a root of a quadratic equation.
- Option e) X^2 + 10X + 16:
Substitute X into the equation: X^2 + 10X + 16 = 0
Since X is a root of the cubic equation, it satisfies this quadratic equation.
Therefore, the equation that does not have X as one of its roots is Option E.
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If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?a)X3 + 4X2 – 32Xb)X2 + 18X + 80c)X2 – 12X + 20d)X2 + 5X – 14e)X2 + 10X + 16Correct answer is option 'E'. Can you explain this answer?
Question Description
If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?a)X3 + 4X2 – 32Xb)X2 + 18X + 80c)X2 – 12X + 20d)X2 + 5X – 14e)X2 + 10X + 16Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?a)X3 + 4X2 – 32Xb)X2 + 18X + 80c)X2 – 12X + 20d)X2 + 5X – 14e)X2 + 10X + 16Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?a)X3 + 4X2 – 32Xb)X2 + 18X + 80c)X2 – 12X + 20d)X2 + 5X – 14e)X2 + 10X + 16Correct answer is option 'E'. Can you explain this answer?.
If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?a)X3 + 4X2 – 32Xb)X2 + 18X + 80c)X2 – 12X + 20d)X2 + 5X – 14e)X2 + 10X + 16Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?a)X3 + 4X2 – 32Xb)X2 + 18X + 80c)X2 – 12X + 20d)X2 + 5X – 14e)X2 + 10X + 16Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X is a root of the equation a3 +8a2 – 20a, than which of the following equations Don’t have the root X as one of their roots?a)X3 + 4X2 – 32Xb)X2 + 18X + 80c)X2 – 12X + 20d)X2 + 5X – 14e)X2 + 10X + 16Correct answer is option 'E'. Can you explain this answer?.
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