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प्रश्न
Find the roots of the following quadratic equation by the factorisation method:
`2x^2 + 5/3x - 2 = 0`
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उत्तर
Given equation is `2x^2 + 5/3x - 2` = 0
On multiplying by 3 on both sides, we get
6x2 + 5x – 6 = 0
⇒ 6x2 + (9x – 4x) – 6 = 0 ....[By splitting the middle term]
⇒ 6x2 + 9x – 4x – 6 = 0
⇒ 3x(2x + 3) – 2(2x + 3) = 0
⇒ (2x + 3)(3x – 2) = 0
Now, 2x + 3 = 0
⇒ x = `-3/2`
And 3x – 2 = 0
⇒ x = `2/3`
Hence, the roots of the equation 6x2 + 5x – 6 = 0 are `(-3)/2` and `2/3`.
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