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If α, β are the roots of the equation 2x2 - 3x + 2 = 0, form the equation whose roots are α2, β2 ?
- a)4x2 – x + 4 = 0
- b)2x2 + x + 5 = 0
- c)5x2 + 3x + 7 = 0
- d)6x2 + 4x + 8 = 0
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If α, β are the roots of the equation 2x2- 3x + 2 = 0, form...
As per the given data
⇒ α + β = - b/a = - ( - 3)/2 = 3/2
⇒ αβ = c/a = 2/2 = 1
For the new equation roots are α2 and β2
∴ sum of the roots α2 + β2 = (α + β)2 - 2αβ = (3/2)2 - 2(1) = 9/4 – 2 = ¼
Product of the roots = α2β2 = (αβ)2 = 12 = 1
⇒ Required equation = x2 – (sum of the roots)x + product of the roots = 0
⇒ x2 – (1/4)x + 1 = 0
⇒ 4x2 - x + 4 = 0
⇒ α + β = - b/a = - ( - 3)/2 = 3/2
⇒ αβ = c/a = 2/2 = 1
For the new equation roots are α2 and β2
∴ sum of the roots α2 + β2 = (α + β)2 - 2αβ = (3/2)2 - 2(1) = 9/4 – 2 = ¼
Product of the roots = α2β2 = (αβ)2 = 12 = 1
⇒ Required equation = x2 – (sum of the roots)x + product of the roots = 0
⇒ x2 – (1/4)x + 1 = 0
⇒ 4x2 - x + 4 = 0
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If α, β are the roots of the equation 2x2- 3x + 2 = 0, form...
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If α, β are the roots of the equation 2x2- 3x + 2 = 0, form the equation whose roots are α2, β2?a)4x2– x + 4 = 0b)2x2+ x + 5 = 0c)5x2+ 3x + 7 = 0d)6x2+ 4x + 8 = 0Correct answer is option 'A'. Can you explain this answer?
Question Description
If α, β are the roots of the equation 2x2- 3x + 2 = 0, form the equation whose roots are α2, β2?a)4x2– x + 4 = 0b)2x2+ x + 5 = 0c)5x2+ 3x + 7 = 0d)6x2+ 4x + 8 = 0Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If α, β are the roots of the equation 2x2- 3x + 2 = 0, form the equation whose roots are α2, β2?a)4x2– x + 4 = 0b)2x2+ x + 5 = 0c)5x2+ 3x + 7 = 0d)6x2+ 4x + 8 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α, β are the roots of the equation 2x2- 3x + 2 = 0, form the equation whose roots are α2, β2?a)4x2– x + 4 = 0b)2x2+ x + 5 = 0c)5x2+ 3x + 7 = 0d)6x2+ 4x + 8 = 0Correct answer is option 'A'. Can you explain this answer?.
If α, β are the roots of the equation 2x2- 3x + 2 = 0, form the equation whose roots are α2, β2?a)4x2– x + 4 = 0b)2x2+ x + 5 = 0c)5x2+ 3x + 7 = 0d)6x2+ 4x + 8 = 0Correct answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about If α, β are the roots of the equation 2x2- 3x + 2 = 0, form the equation whose roots are α2, β2?a)4x2– x + 4 = 0b)2x2+ x + 5 = 0c)5x2+ 3x + 7 = 0d)6x2+ 4x + 8 = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α, β are the roots of the equation 2x2- 3x + 2 = 0, form the equation whose roots are α2, β2?a)4x2– x + 4 = 0b)2x2+ x + 5 = 0c)5x2+ 3x + 7 = 0d)6x2+ 4x + 8 = 0Correct answer is option 'A'. Can you explain this answer?.
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