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Quadratic Equations
Quadratic equations represent any equation that can be rearranged in standard forma (ax² + bx + c( =0(a, b & c) are known.
Quadratic equations can always be solved using the quadratic formula, but sometimes factoring or isolating the variable is also posible.
In the square equation ax² + bx + c = 0
- a = 1
- b = 5
- c = 2
[tex]\boldsymbol{\sf{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} \ ,\Delta=b^{2}-4ac } }[/tex]
Let's calculate the discriminant of the quadratic equation:
- ∆ = b² - 4ac = 5² - 4 1 2 = 25 - 8 = 17
Since the discriminant is greater than zero, then the quadratic equation has two real roots.
[tex]\boldsymbol{\sf{x_{1}=\dfrac{-b-\sqrt{\Delta} }{ 2\cdot a}=\dfrac{-5-\sqrt{17} }{2\cdot1} }}[/tex]
[tex]\boldsymbol{\sf{x_{2}=\dfrac{-b+\sqrt{\Delta} }{ 2\cdot a}=\dfrac{-5+\sqrt{17} }{2\cdot1} }}[/tex]
Solution:
[tex]\boldsymbol{\sf{x=\dfrac{-5\pm\sqrt{17} }{2} }}[/tex]
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