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Question
Solve using formula.
x2 + 6x + 5 = 0
Solution
x2 + 6x + 5 = 0
On comparing with the equation
\[a x^2 + bx + c = 0\]
a = 1, b = 6 and c = 5
Now
= b2 - 4ac
= 62 - 4 × 1 × 5
= 36 - 20
= 16
\[x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}\]
\[x = \frac{- 6 \pm \sqrt{16}}{2 \times 1} = \frac{- 6 \pm 4}{2}\]
\[ \Rightarrow x = \frac{- 6 + 4}{2} \text{ or } x = \frac{- 6 - 4}{2}\]
x = `(-2)/2` or x = `(-10)/2`
\[ \Rightarrow x = - 1 \text{ or } x = - 5\]
∴ -1 and -5 are roots of the given quadratic equation.
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Let α = 2 and β = 5 are the roots of the quadratic equation.
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