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Question
Solve the following quadratic equation.
x2 - 4x - 3 = 0
Solution
x2 - 4x - 3 = 0
Δ = b2 - 4ac
= (-4)2 - 4(1)(-3)
= 16 + 12
= 28
\[\Rightarrow x = \frac{- \left( - 4 \right) \pm \sqrt{\left( - 4 \right)^2 - 4 \times 1 \times \left( - 3 \right)}}{2 \times 1}\]
\[ \Rightarrow x = \frac{4 \pm \sqrt{16 + 12}}{2}\]
\[ \Rightarrow x = \frac{4 \pm \sqrt{28}}{2}\]
\[ \Rightarrow x = \frac{4 \pm 2\sqrt{7}}{2}\]
\[ \Rightarrow x = 2 \pm \sqrt{7}\]
The roots of the given quadratic equation are
`2+sqrt7 and 2-sqrt7`
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