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If mx2 + nx + c = 0 and px2 + qx + r = 0 have one root in common. If the sum and product of the roots which are different are 0 and 1 respectively, then what is the value of 
?
?- a)2np
- b)4mp
- c)2rc
- d)4nq
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If mx2 + nx + c = 0 and px2 + qx + r = 0 have one root in common. If t...
Let α, β be the roots of mx2 + nx + c = 0 and y, 6 be the roots of px2 + qx + r = 0
As these two quadratic equations have one root in common, let us assume that α = γ
Adding (i) and (iii), we get,
But, β + δ = 0
Multiplying (ii) and (iv), we get,
But, βδ = 1
Eliminating α from (v) and (vi), we get,
∴ 4crmp = [(-np) + (-mq)]2
∴ 4crmp = [n2p2 + m2q2 + 2npmq]
∴ 4 crmp - 4npmq = [n2p2+m2q2 - 2npmq]
∴ 4mp(cr - nq) = [np - mq]2
Hence, option 2.
As these two quadratic equations have one root in common, let us assume that α = γ
Adding (i) and (iii), we get,
But, β + δ = 0
Multiplying (ii) and (iv), we get,
But, βδ = 1
Eliminating α from (v) and (vi), we get,
∴ 4crmp = [(-np) + (-mq)]2
∴ 4crmp = [n2p2 + m2q2 + 2npmq]
∴ 4 crmp - 4npmq = [n2p2+m2q2 - 2npmq]
∴ 4mp(cr - nq) = [np - mq]2
Hence, option 2.
Most Upvoted Answer
If mx2 + nx + c = 0 and px2 + qx + r = 0 have one root in common. If t...
Let α, β be the roots of mx2 + nx + c = 0 and y, 6 be the roots of px2 + qx + r = 0
As these two quadratic equations have one root in common, let us assume that α = γ
Adding (i) and (iii), we get,
But, β + δ = 0
Multiplying (ii) and (iv), we get,
But, βδ = 1
Eliminating α from (v) and (vi), we get,
∴ 4crmp = [(-np) + (-mq)]2
∴ 4crmp = [n2p2 + m2q2 + 2npmq]
∴ 4 crmp - 4npmq = [n2p2+m2q2 - 2npmq]
∴ 4mp(cr - nq) = [np - mq]2
Hence, option 2.
As these two quadratic equations have one root in common, let us assume that α = γ
Adding (i) and (iii), we get,
But, β + δ = 0
Multiplying (ii) and (iv), we get,
But, βδ = 1
Eliminating α from (v) and (vi), we get,
∴ 4crmp = [(-np) + (-mq)]2
∴ 4crmp = [n2p2 + m2q2 + 2npmq]
∴ 4 crmp - 4npmq = [n2p2+m2q2 - 2npmq]
∴ 4mp(cr - nq) = [np - mq]2
Hence, option 2.
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If mx2 + nx + c = 0 and px2 + qx + r = 0 have one root in common. If the sum and product of the roots which are different are 0 and 1 respectively, then what is the value of ?a)2npb)4mpc)2rcd)4nqCorrect answer is option 'B'. Can you explain this answer?
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