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Question
Math
Posted 6 months ago
Find the zeros of the function.
Enter the solutions from least to greatest.
g(x)=10x2+490
g(x)=-10 x^{2}+490

lesser x=x= \square
greater x=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)=10x2+490g(x) = -10x^2 + 490, set the function equal to zero: 10x2+490=0-10x^2 + 490 = 0
step 2
Divide both sides of the equation by 10-10 to simplify: x249=0x^2 - 49 = 0
step 3
Factor the left side of the equation as a difference of squares: (x+7)(x7)=0(x + 7)(x - 7) = 0
step 4
Set each factor equal to zero and solve for xx: x+7=0x + 7 = 0 or x7=0x - 7 = 0
step 5
Solving x+7=0x + 7 = 0 gives x=7x = -7
step 6
Solving x7=0x - 7 = 0 gives x=7x = 7
Answer
lesser x=7x=-7
greater x=7x=7
Key Concept
Finding zeros of a quadratic function
Explanation
The zeros of the function are the values of xx for which the function equals zero. These are found by factoring the quadratic equation and solving for xx.

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