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Question
Solve the following equation using quadratic formula:
`3/4 x^2 - x - 1 = 0`
Sum
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Solution
Comparing equation `3/4 x^2 - x - 1 = 0` with ax2 + bx + c = 0, we get:
a = `3/4`, b = –1 and c = –1
By formula,
`x = (-b ± sqrt(b^2 - 4ac))/(2a)`
Substituting values we get:
⇒ `x = (-(-1) ± sqrt((-1)^2 - 4(3/4)(-1)))/(2(3/4))`
= `(1 ± sqrt(1 + 3))/((3/2))`
= `(1 ± sqrt(4))/((3/2))`
= `(1 ± 2)/((3/2))`
= `(2(1 ± 2))/3`
= `(2 ± 4)/3`
= `(2 + 4)/3` or `(2 - 4)/3`
= `6/3` or `(-2)/3`
= 2 or `(-2)/3`
Hence, `x = {2, (-2)/3}`.
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