Question

Math

Posted 6 months ago

```
Find the zeros of the function.
Enter the solutions from least to greatest.
$g(x)=-10 x^{2}+490$
lesser $x=$ $\square$
greater $x=$ $\square$
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To find the zeros of the function $g(x) = -10x^2 + 490$, set the function equal to zero: $-10x^2 + 490 = 0$

step 2

Divide both sides of the equation by $-10$ to simplify: $x^2 - 49 = 0$

step 3

Factor the left side of the equation as a difference of squares: $(x + 7)(x - 7) = 0$

step 4

Set each factor equal to zero and solve for $x$: $x + 7 = 0$ or $x - 7 = 0$

step 5

Solving $x + 7 = 0$ gives $x = -7$

step 6

Solving $x - 7 = 0$ gives $x = 7$

Answer

lesser $x=-7$

greater $x=7$

Key Concept

Finding zeros of a quadratic function

Explanation

The zeros of the function are the values of $x$ for which the function equals zero. These are found by factoring the quadratic equation and solving for $x$.

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