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प्रश्न
Solve the following quadratic equation:
8x2 + 2x + 1 = 0
उत्तर
Given equation is 8x2 + 2x + 1 = 0
Comparing with ax2 + bx + c = 0, we get
a = 8, b = 2, c = 1
Discriminant = 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`
∴ x = `(-1 ± sqrt(7)"i")/8`
∴ The roots of the given equation are `(-1 + sqrt(7)"i")/8 and (-1 - sqrt(7)"i")/8`.
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