How do you solve #x^2-x+3=0# using the quadratic formula?
The quadratic formula provides the roots for this:
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To solve the quadratic equation ( x^2 - x + 3 = 0 ) using the quadratic formula, where the equation is in the form ( ax^2 + bx + c = 0 ), follow these steps:
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Identify the coefficients ( a ), ( b ), and ( c ). ( a = 1 ), ( b = -1 ), ( c = 3 ).
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Substitute the values of ( a ), ( b ), and ( c ) into the quadratic formula: [ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ]
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Plug in the values: [ x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4 \cdot 1 \cdot 3}}}}{{2 \cdot 1}} ]
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Simplify inside the square root: [ x = \frac{{1 \pm \sqrt{{1 - 12}}}}{2} ] [ x = \frac{{1 \pm \sqrt{{-11}}}}{2} ]
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Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, ( x ) is not a real number.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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