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प्रश्न
Solve the following quadratic equation.
8x2 + 2x + 1 = 0
उत्तर
Comparing the equation 8x2 + 2x + 1 = 0 with ax2 +bx + c = 0, we have,
a = 8, b = 2, c = 1
∴ b2 – 4ac = (2)2 – 4(8)(1)
= 4 – 32
= – 28 < 0
So, the given equation has complex roots. These roots are given by
x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`
= `(-2 ± sqrt(-28))/(2(8))`
= `(-2 ± 2sqrt(7)"i")/16`
= `(-1 + sqrt(7)"i")/8`
Hence, the roots of the equation are
`(-1 + sqrt(7)"i")/8` and `(-1 - sqrt(7)"i")/8`.
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