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1. Using quadratic formula, what are the roots of x² + 2x - 2=0?​

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KAntoineDoixidn

✏️ QUADRATIC

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[tex] \large \bold{\blue{PROBLEM:}} [/tex] Using quadratic formula, what are the roots of...

  • [tex] x^2 + 2x - 2=0 [/tex]

[tex] \large \bold{\blue{SOLUTION:}} [/tex] Identify the values of a, b, and c in standard form.

  • [tex] \boxed{ax^2 + bx + c = 0} [/tex]

  • [tex] a = 1, \: b = 2, \: c = -2 [/tex]

» Use the quadratic formula to identify its roots.

  • [tex] \boxed{x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}} \\ [/tex]

  • [tex] x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-2)}}{2(1)} \\ [/tex]

  • [tex] x = \frac{-2 \pm \sqrt{4 + 8}}{2} \\ [/tex]

  • [tex] x = \frac{-2 \pm \sqrt{12}}{2} \\ [/tex]

  • [tex] x = \frac{-2 \pm 2\sqrt{3}}{2} \\ [/tex]

  • [tex] x = \frac{\cancel2(-1 \pm \sqrt{3})}{\cancel2} \\ [/tex]

  • [tex] x = -1 \pm \sqrt{3} [/tex]

[tex] \large \therefore \underline{\boxed{\tt \purple{x = -1 + \sqrt3, \: x = -1 - \sqrt3}}} [/tex]

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UK2019idn

✏️QUADRATIC EQUATION

What are the roots of x² + 2x - 2 = 0?

- The standard form of a quadratic equation is ax² + bx + c = 0, where a, b are the coefficients, x is the variable, and c is the constant term.

  • [tex]\sf{{x² + 2x - 2 = 0}}[/tex]

- Using the Quadratic Formula where a = 1, b = 2, and c = -2

  • [tex]\huge \sf{{x = \frac {-b \: ± \: \sqrt{ {b}^{2} - 4ac} } {2a}}} [/tex]

- Substitute all the given

  • [tex]\large \sf{{x = \frac {-2 \: ± \: \sqrt{ {2}^{2} \: - \: 4(1)( - 2)}} {2(1)}}} [/tex]

  • [tex]\large \sf{{x = \frac {-2 \: ± \: \sqrt{4 - ( - 8)} } {2}}} [/tex]

  • [tex]\large \sf{{x = \frac {-2 \: ± \: \sqrt{12} } {2}}} [/tex]

- Simplify the Radical

  • [tex]\large \sf{{x = \frac {-2 \: ± \: 2 \sqrt{3} } {2}}} [/tex]

  • [tex]\large \sf{{x = \frac {-2}{2} ±\frac{ \cancel2 \sqrt{3} } {\cancel2}}} [/tex]

  • [tex]\large \sf{{x = - 1±{ } { \sqrt{3}}}} [/tex]

[tex]\large \underline{\boxed{\tt \blue {Therefore \: the \: answer \: is \: {\green{x = - 1 + \sqrt{3} , - 1 - \sqrt{3} }}}}} [/tex]

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