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Oksanka [162]
3 years ago
13

PLS HELP ! Will give brainliest!

Mathematics
1 answer:
Rasek [7]3 years ago
3 0

Given:

The quadratic equation is :

16x^2-20x-6=0

To find:

The quadratic formula for the given equation after substituting the values.

Solution:

If a quadratic equation is ax^2+bx+c=0, then the quadratic formula is:

x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

We have,

16x^2-20x-6=0

In this equation, a=16,b=-20,c=-6.

Substituting a=16,b=-20,c=-6 in the above formula, we get

x=\dfrac{-(-20)\pm \sqrt{(-20)^2-4(16)(-6)}}{2(16)}

Therefore, the required quadratic formula for the given equation after substituting the values is x=\dfrac{-(-20)\pm \sqrt{(-20)^2-4(16)(-6)}}{2(16)}.

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\sf 3 \underset{+1}{\longrightarrow} 4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19

As the first differences are <u>not the same</u>, we need to calculate the <u>second differences</u>:

\sf 1 \underset{+2}{\longrightarrow} 3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7

As the second differences are the <u>same</u>, the relationship between the variable is quadratic and will contain an x^2  term.

--------------------------------------------------------------------------------------------------

<u>To determine the quadratic equation</u>

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As the second difference is 2, and half of 2 is 1, the coefficient of x^2 is 1.

The standard form of a quadratic equation is:  y=ax^2+bx+c

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We have already determined that the coefficient of x^2 is 1.

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From the given table, when x=0, y=12.

\implies a(0)^2+b(0)+c=12

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Therefore, the quadratic equation for the given ordered pairs is:

y=x^2+6x+12

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