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If α and β are the roots of the equation 3x 2 - 11x + 6 = 0, then find the equation whose roots are ( βα )and ( α- β ). [ α > β ]

If α and β are the roots of the equation 3x2 - 11x + 6 = 0, then find the equation whose roots are (βα)and (α-β). [α >β]

Grade:10

1 Answers

Khimraj
3007 Points
6 years ago
= αβ = 6/3 = 2roduct of roots pα + β = 11/3Then sum of roots = α and β are the roots of the equation 3x2 - 11x + 6 = 0
αβ]1/2 = 7/3α-β = [(α+β)2-4
Let another equation is ax2+bx+c=0
other equation has root βα and α-β
Then sum of roots = -b/a = βα +(α-β) = 2 + 7/3 = 13/3
product of roots = c/a = βα*(α-β) = 14/3.
So equation is 3x2-13x+14 = 0.
Hope it clears. If you like answer then please approve it.

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