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Question
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Solution
We have
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Here, `a = (4)/(3), b = -2 and c = (3)/(4)`
Discriminant
= b2 - 4ac
= (-2)2 -4 x `(4)/(3) xx (3)/(4)`
= 4 - 4
= 0
So, the given equation has two real and equal roots given by
a = `(-b + sqrt(b^2 - 4ac))/(2a)`
= `(+ 2 + 0)/(4)`
= `(3)/(4)`
and β = `(-b - sqrt(b^2 - 4ac))/(2a)`
= `(+ 2 - 0)/(2 xx (4)/(3))`
= `(3)/(4)`.
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