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प्रश्न
Solve the following equation by using formula :
(2x + 3)(3x – 2) + 2 = 0
उत्तर
(2x + 3)(3x – 2) + 2 = 0
6x2 - 4x + 9x - 6 + 2 = 0
6x2 + 5x - 4 = 0
Here a = 6, b = 5, c = -4
D = b2 - 4ac
= (5)2 - 4 x 6 x (-4)
= 25 + 96
= 121
∵ x = `(-b + sqrt("D"))/(2a)`
= `(-5 ± sqrt(121))/(5 xx 6)`
= `(-5 ±11)/(12)`
∴ x1 = `(-5 + 11)/(12)`
= `(6)/(12)`
= `(1)/(2)`
∴ x2 = `(-5 - 11)/(12)`
= `(-16)/(12)`
= `(-4)/(3)`
Hence x = `(1)/(2), (-4)/(3)`.
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