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Let α,β be the zeros of the polynomial x2 – px + r and    be the zeros of x2 – qx + r. Then the value
of r is –
  • a)
     (p - q)(2q - p)
  • b)
    (q - p)(2p - q)
  • c)
    (q - 2p)(2q - p)
  • d)
    (2p - q)(2q - p)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let α,βbe the zeros of the polynomial x2– px + r and ...
alpha and beta as a,b (it's Easy to solve it)
So,Since a and b are roots of 
We can say a+b=p...say eq1 and ab=r
Also a/2 and 2b are roots of 
So, a/2 +2b=q .... say eq2 and a/2*2b=ab=r
2(eq1)-eq2=2a -a/2 +2b-2b=2p-q
so 3a/2=2p-q
a=2(2p-q)/3
Substituting in eq1
We get b=p-4p/3+2q/3=(2q-p)/3
So we know ab=r=2(2p-q)(2q-p)/9

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Most Upvoted Answer
Let α,βbe the zeros of the polynomial x2– px + r and ...
Since a and b are roots of  x2 – px + r = 0 
We can say a+b=p....say equation 1 and ab=r
Also a/2 and 2b are roots of  x2 – qx + r  
So, a/2 +2b=q ..... say equation 2 and a/2*2b=ab=r
2(equation1)-equation 2 = 2a -a/2 +2b-2b = 2p-q
so 3a/2=2p-q
a=2(2p-q)/3
Substituting in equation 1
We get b=p-4p/3+2q/3=(2q-p)/3
So we know ab=r=2(2p-q)(2q-p)/9
Free Test
Community Answer
Let α,βbe the zeros of the polynomial x2– px + r and ...
Option D is correct...
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Let α,βbe the zeros of the polynomial x2– px + r and be the zeros of x2– qx + r. Then the valueof r is –a)(p - q)(2q - p)b)(q - p)(2p - q)c)(q - 2p)(2q - p)d)(2p - q)(2q - p)Correct answer is option 'D'. Can you explain this answer?
Question Description
Let α,βbe the zeros of the polynomial x2– px + r and be the zeros of x2– qx + r. Then the valueof r is –a)(p - q)(2q - p)b)(q - p)(2p - q)c)(q - 2p)(2q - p)d)(2p - q)(2q - p)Correct answer is option 'D'. 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 Let α,βbe the zeros of the polynomial x2– px + r and be the zeros of x2– qx + r. Then the valueof r is –a)(p - q)(2q - p)b)(q - p)(2p - q)c)(q - 2p)(2q - p)d)(2p - q)(2q - p)Correct answer is option 'D'. 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 Let α,βbe the zeros of the polynomial x2– px + r and be the zeros of x2– qx + r. Then the valueof r is –a)(p - q)(2q - p)b)(q - p)(2p - q)c)(q - 2p)(2q - p)d)(2p - q)(2q - p)Correct answer is option 'D'. Can you explain this answer?.
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