State the concept of quadratic equation with the help of an activity.
Answers
Step-by-step explanation:
Use the Quadratic Formula to solve x2 – 4x – 8 = 0
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The Quadratic Formula requires that I have the quadratic expression on one side of the "equals" sign, with "zero" on the other side. They've given me the equation already in that form. Also, the Formula is stated in terms of the numerical coefficients of the terms of the quadratic expression. Looking at the coefficients in this equation, I see that a = 1, b = –4, and c = –8. I'll plug these numbers into the Formula, and simplify. (I should get the same answer as I previously have.)
\small{ x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-8)\phantom{\big|}}}{2(1)} }x=
2(1)
−(−4)±
(−4)
2
−4(1)(−8)
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\small{ = \dfrac{4 \pm \sqrt{16 + 32\phantom{\big|}}}{2} = \dfrac{4 \pm \sqrt{48\phantom{\big|}}}{2} }=
2
4±
16+32
∣
∣
∣
=
2
4±
48
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\small{ = \dfrac{4 \pm \sqrt{16 \cdot 3\,}}{2} = \dfrac{4 \pm 4 \sqrt{3\,}}{2} }=
2
4±
16⋅3
=
2
4±4
3
\small{ = \dfrac{2 \left(2 \pm 2 \sqrt{3\phantom{|}}\right)}{2} = 2 \pm 2 \sqrt{3\,} }=
2
2(2±2
3∣
)
=2±2
3
This is the same answer as I got before, which confirms that the Quadratic Formula works as intended. Once again, my final answer is:
\mathbf{\color{purple}{\small{ \mathit{x} = 2 \pm 2 \sqrt{3\phantom{|}} }}}x=2±2
3∣