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Consider the following quadratic function. Y=x^2-7x+12Find the real zeros, if any, of this function. Reduce all fractions to lowest terms.

Consider the following quadratic function. Y=x^2-7x+12Find the real zeros, if any-example-1
User KaoriYui
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1 Answer

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\mleft(3,0\mright)and(4,0)

Step-by-step explanation

The zeros of a polynomial are the values of x which satisfy the equation y = f(x). Here f(x) is a function of x, and the zeros of the polynomial is the values of x for which the y value is equal to zero

so

Step 1

when the graph crosses the x-axis

let y=0

so


\begin{gathered} y=x^2-7x+12 \\ \end{gathered}

The middle number is -7 and the last number is 12.

Factoring means we want something like


\begin{gathered} \mleft(x+_{}\mright)\mleft(x+_{}\mright) \\ \end{gathered}

We need two numbers that...

Add together to get -7

Multiply together to get 12

so, the number are


\begin{gathered} -3\text{ and -4} \\ so \end{gathered}


\begin{gathered} y=(x-3_{})(x-4_{}) \\ 0=(x-3_{})(x-4_{}) \end{gathered}

so, the solutions are

x=3

and

x=4

(3,0) and (4,0)

I hope this helps you

User Senem
by
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