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If α+β=−2 and α33=−56, then the quadratic equation whose roots are α and β is
  • a)
    x2+2x−16=0
  • b)
    x2+2x+15=0
  • c)
    x2+2x−12=0
  • d)
    x2+2x−8=0
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If α+β=−2 and α3+β3=−56, then the qu...
Given that, α+β=−2 and α33=−56
So, Quadratic equation whose roots are α and β will be given by
x2−(α+β)x+αβ=0  ...(1)
We are given with the sum of roots, so finding product of roots,
∵ α33=−56
⇒(α+β)(α2+β2−αβ)=−56
⇒α2+β2−αβ= - 28 [α + β = -2]
⇒α2+β2=28+αβ  ...(2)
Now,  (α+β)2=(−2)2
⇒α2+β2+2αβ=4
⇒28+3αβ=4 (from equation (2)

Thus, from equation (1), required quadratic equation is given as
x2−(−2)x+(−8)=0
⇒x2+2x−8=0
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If α+β=−2 and α3+β3=−56, then the quadratic equation whose roots are α and β isa)x2+2x−16=0b)x2+2x+15=0c)x2+2x−12=0d)x2+2x−8=0Correct answer is option 'D'. Can you explain this answer?
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If α+β=−2 and α3+β3=−56, then the quadratic equation whose roots are α and β isa)x2+2x−16=0b)x2+2x+15=0c)x2+2x−12=0d)x2+2x−8=0Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If α+β=−2 and α3+β3=−56, then the quadratic equation whose roots are α and β isa)x2+2x−16=0b)x2+2x+15=0c)x2+2x−12=0d)x2+2x−8=0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α+β=−2 and α3+β3=−56, then the quadratic equation whose roots are α and β isa)x2+2x−16=0b)x2+2x+15=0c)x2+2x−12=0d)x2+2x−8=0Correct answer is option 'D'. Can you explain this answer?.
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