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Question
Find the values of m for which equation 3x2 + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.
Solution
Given quadratic equation is 3x2 + mx + 2 = 0 ...(i)
The quadratic equation has equal roots if its discriminant is zero
`=>` D = b2 – 4ac = 0
`=>` m2 – 4(2)(3) = 0
`=>` m2 = –24
When `m = 2sqrt(6)`, equation (i) becomes
`3x^2 + 2sqrt(6)x + 2 = 0`
`=> (sqrt(3)x + sqrt(2))^2 = 0`
`=> x = sqrt2/sqrt3`
= `-sqrt(2)/sqrt(3) xx sqrt(3)/sqrt(3)`
= `-sqrt(6)/3`
When `m = -2sqrt(6)`, equation (i) becomes
x = `-sqrt(6)/3, sqrt(6)/3`
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