Answer:
[tex]x_{1,2}=\frac{-2(+-)\sqrt{2^{2}-4(4)(-1)}}{2(4)}[/tex]
Step-by-step explanation:
The given expression is
[tex]0=4x^{2} +2x-1[/tex]
Which is a standard form of a quadratic equation, like [tex]ax^{2} +bx+c=0[/tex]
So, each letter is equal to
[tex]a=4\\b=2\\c=-1[/tex]
Now, the quadratic formula is
[tex]x_{1,2}=\frac{-b(+-)\sqrt{b^{2}-4ac}}{2a}[/tex]
Replacing each value, we have
[tex]x_{1,2}=\frac{-2(+-)\sqrt{2^{2}-4(4)(-1)}}{2(4)}[/tex]
Notice that this expression with all values replaced coincides with the last choice.
Therefore, the last choice is the right answer.
[tex]x_{1,2}=\frac{-2(+-)\sqrt{2^{2}-4(4)(-1)}}{2(4)}[/tex]
The correct substitution into the quadratic equation is [tex]x=\frac{-2\pm \sqrt{2^2-4(4)(-1)} }{2(4)}[/tex]
A quadratic equation is a polynomial of degree 2. It is represented as:
y = ax² + bx + c
Given the equation:
4x² + 2x - 1 = 0
a = 4, b = 2, c = -1
Hence:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\substituting:\\\\x=\frac{-2\pm \sqrt{2^2-4(4)(-1)} }{2(4)} \\\\[/tex]
The correct substitution into the quadratic equation is [tex]x=\frac{-2\pm \sqrt{2^2-4(4)(-1)} }{2(4)}[/tex]
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