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प्रश्न
Solve the following quadratic equation:
x2 – 4x + 13 = 0
उत्तर
Given equation is x2 – 4x + 13 = 0
Comparing with ax2 + bx + c = 0, we get
a = 1, b = –4, c = 13
Discriminant = b2 – 4ac
= (– 4)2 – 4 × 1 × 13
= 16 – 52
= –36 < 0
So, the given equation has complex roots.
These roots are given by
x = `(-"b" ± sqrt("b"^2 - 4"ac"))/(2"a")`
= `(-(- 4) ± sqrt(- 36))/(2 1)`
= `(4 ± 6"i")/2`
= 2 ± 6i
∴ The roots of the given equation are 2 + 6i and 2 – 6i.
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