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प्रश्न
Solve the following equation using quadratic formula:
`2x^2 + sqrt(7)x - 7 = 0`
बेरीज
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उत्तर
Comparing equation `2x^2 + sqrt(7)x - 7 = 0` with ax2 + bx + c = 0, we get:
a = 2, b = `sqrt(7)` and c = –7
By formula,
`x = (-b ± sqrt(b^2 - 4ac))/(2a)`
Substituting values we get:
⇒ `x = (-(sqrt(7)) ± sqrt((sqrt(7))^2 - 4 xx 2 xx (-7)))/(2 xx 2)`
= `(-sqrt(7) ± sqrt(7 + 56))/4`
= `(-sqrt(7) ± sqrt(63))/4`
= `(-sqrt(7) ± sqrt(7 xx 9))/4`
= `(-sqrt(7) ± 3sqrt(7))/4`
= `(-sqrt(7) + 3sqrt(7))/4` or `(-sqrt(7) - 3sqrt(7))/4`
= `(2sqrt(7))/4` or `(-4sqrt(7))/4`
= `sqrt(7)/2` or `-sqrt(7)`
Hence, `x = {-sqrt(7), sqrt(7)/2}`.
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