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If α,β are the roots of the polynomial x2 – px + q, then the quadratic polynomial, the roots of which are (α2– β2) (α3 – β3) and (α3β2 + α2β3) :
  • a)
    px2 – (5p + 7q) x – (p6q6 + 4p2q6) = 0
  • b)
    x2 – (p5 – 5p3q + 5pq2) x + (p6q2 – 5p4q3 + 4p2q4) = 0
  • c)
    x2 – (p3q – 5p5 + p4q) – (p6q2 – 5p2q6) = 0
  • d)
    All of the above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If α,βare the roots of the polynomial x2– px + q, the...
If α,β are the roots of the polynomial x2 - px + q.

α + β = p and αβ = q

if the roots are (α22)(α3 - β3) and (α3β2 + α2β3)

= (α22)(α3 - β3) + (α3β2 + α2β3)

= (α +β)(α -β)2(α2 + αβ+ β2) + α2β2(α + β).

= (α +β)[ (α +β)2 - 4αβ ] [ (α +β)2 - αβ ] + α2β2(α + β).

= p( p2 - 4q)( p2 - q) + q2p

= p( p4 - p2q -4p2q + 4q2) + pq2

= p5 - 5p3q + 5pq2 .

⇒ (α22)(α3 - β3)(α3β2 + α2β3) = (p6q2-5p4q3+4p2q4)

∴ x2- (p5 - 5p3q + 5pq2 ) x + ( p6q2 - 5p4q3 + 4p2q4 ) = 0
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If α,βare the roots of the polynomial x2– px + q, the...
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If α,βare the roots of the polynomial x2– px + q, then the quadratic polynomial, the roots of which are (α2– β2) (α3– β3) and (α3β2+ α2β3) :a)px2– (5p + 7q) x – (p6q6+ 4p2q6) = 0b)x2– (p5– 5p3q + 5pq2) x + (p6q2– 5p4q3+ 4p2q4) = 0c)x2– (p3q – 5p5+ p4q) – (p6q2– 5p2q6) = 0d)All of the aboveCorrect answer is option 'B'. Can you explain this answer?
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If α,βare the roots of the polynomial x2– px + q, then the quadratic polynomial, the roots of which are (α2– β2) (α3– β3) and (α3β2+ α2β3) :a)px2– (5p + 7q) x – (p6q6+ 4p2q6) = 0b)x2– (p5– 5p3q + 5pq2) x + (p6q2– 5p4q3+ 4p2q4) = 0c)x2– (p3q – 5p5+ p4q) – (p6q2– 5p2q6) = 0d)All of the aboveCorrect answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If α,βare the roots of the polynomial x2– px + q, then the quadratic polynomial, the roots of which are (α2– β2) (α3– β3) and (α3β2+ α2β3) :a)px2– (5p + 7q) x – (p6q6+ 4p2q6) = 0b)x2– (p5– 5p3q + 5pq2) x + (p6q2– 5p4q3+ 4p2q4) = 0c)x2– (p3q – 5p5+ p4q) – (p6q2– 5p2q6) = 0d)All of the aboveCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If α,βare the roots of the polynomial x2– px + q, then the quadratic polynomial, the roots of which are (α2– β2) (α3– β3) and (α3β2+ α2β3) :a)px2– (5p + 7q) x – (p6q6+ 4p2q6) = 0b)x2– (p5– 5p3q + 5pq2) x + (p6q2– 5p4q3+ 4p2q4) = 0c)x2– (p3q – 5p5+ p4q) – (p6q2– 5p2q6) = 0d)All of the aboveCorrect answer is option 'B'. Can you explain this answer?.
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