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11 months ago

If the leading coefficient of a polynomial function is positive, the graph will go

Mathematics

1 answer:

Greeley [361]11 months ago

7 0

Step-by-step explanation:

the leading coefficient means the coefficient (factor) of the term with the highest exponent of the variable (typically x).

with sufficiently large values of this variable (x - going far enough to the right) this term will "win" in value against any other term of the polynomial expression.

and therefore the sign of its factor (coefficient) will determine, if the curve will go up or down.

a positive factor (coefficient) will make the value of this term and therefore of the whole polynomial larger and larger, making the curve going up to +infinity.

a negative factor (coefficient) will make the value of this term and therefore of the whole polynomial smaller and smaller (more negative and more negative), making the curve going down to -infinity.

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Step-by-step explanation:

You have the quadratic function $2x^2-x+1=0$ to find the solutions for this equation we are going to use Bhaskara's Formula.

For the quadratic functions $ax^2+bx+c=0$ with $a\neq 0$ the Bhaskara's Formula is:

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$x_1=\frac{-b+\sqrt{b^2-4.a.c} }{2.a}\\\\x_1=\frac{-(-1)+\sqrt{(-1)^2-4.2.1} }{2.2}\\\\x_1=\frac{1+\sqrt{1-8} }{4}\\\\x_1=\frac{1+\sqrt{-7} }{4}\\\\x_1=\frac{1+\sqrt{(-1).7} }{4}\\x_1=\frac{1+\sqrt{-1}.\sqrt{7}}{4}$

Observation: $\sqrt{-1}=i$

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$x_2=\frac{-b-\sqrt{b^2-4.a.c} }{2.a}\\\\x_2=\frac{-(-1)-\sqrt{(-1)^2-4.2.1} }{2.2}\\\\x_2=\frac{1-i.\sqrt{7} }{4}\\\\x_2=\frac{1}{4}-(\frac{\sqrt{7}}{4})i$

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