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Svet_ta [14]
2 years ago
7

Let ​f(x)=x^2+6x−16​. Enter the x-intercepts of the quadratic function in the boxes.

Mathematics
1 answer:
Sauron [17]2 years ago
7 0

\underline{\underline{\large\bf{Given:-}}}

\red{\leadsto}\:\textsf{}\sf f(x)= x^2+6x−16

\underline{\underline{\large\bf{To Find:-}}}

\orange{\leadsto}\:\textsf{ x-intercepts of the quadratic function }\sf

\\

\underline{\underline{\large\bf{Solution:-}}}\\

\longrightarrowx- intercept is the point where graph of given function touches the x-axis,f(x) becomes 0 at the point where graph of given function touches the x-axis. Therefore, we would to solve x^2+6x−16=0 and find its root.

\begin{gathered}\\\implies\quad \sf x^2+6x−16=0 \\\end{gathered}

\begin{gathered}\\\implies\quad \sf x^2+8x-2x −16=0 \\\end{gathered}

\begin{gathered}\\\implies\quad \sf x(x+8)-2(x+8)=0 \\\end{gathered}

\begin{gathered}\\\implies\quad \sf (x-2)(x+8)=0\\\end{gathered}

\begin{gathered}\\\implies\quad \sf  x=2\quad or \quad x=-8 \\\end{gathered}

\leadstox-intercepts of the given quadratic function are 2 and -8 .

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