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Question
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
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Solution
Given quadratic equation is 3x2 – 5x + 2 = 0
D = b2 – 4ac
= (–5)2 – 4(3)(2)
= 25 – 24
= 1
Since D > 0, the roots of the given quadratic equation are real and distinct.
Using quadratic formula, we have
`x = (-b ± sqrt(b^2 - 4ac))/(2a)`
`=> x = (5 ± sqrt((-5)^2 - 4(3)(2)))/(2(3)`
`=> x = (5 ± sqrt(25 - 24))/6`
`=> x = (5 ± 1)/6`
`=> x = (5 + 1)/6` or `x = (5 - 1)/6`
`=> x = 6/6` or `x = 4/6`
`=> x = 1` or `x = 2/3`
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