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Grade 12th passDifferential Calculus

If a is not = b,but a^2 = 5a – 3, b^2 = 5b –3, then the equation having a/b and b/a as its roots is –
(A) 3x^2 – 25x + 3 = 0
(B) x^2 + 5x – 3 = 0
(C) x^2 – 5x + 3 = 0
(D) 3x^2 – 19x + 3 = 0

Adeeba Waheed

7 Years agoGrade 12th pass

1 Answer

Aditya Gupta

Approved Tutor Answer7 Years ago

Obviously a and b are roots of the equation

x^2-5x+3=0

Now a+b=5 and ab=3

Also, a/b+b/a= (a^2+b^2)/ab= (a+b)^2/ab - 2= 25/3-2= 19/3 and a/b*b/a= 1.

So equation whose roots are a/b and b/a is

x^2-19x/3+1=0

Or 3x^2-19x+3=0

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