IDNLearn.com makes it easy to get reliable answers from knowledgeable individuals. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.
Sagot :
To determine which of the given quadratic functions has real zeros at [tex]\( x = -10 \)[/tex] and [tex]\( x = -6 \)[/tex], we can use the fact that the roots of a quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] are related to its factors.
When a quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] has roots [tex]\( \alpha \)[/tex] and [tex]\( \beta \)[/tex], it can be written in the factored form as:
[tex]\[ a (x - \alpha) (x - \beta) = 0 \][/tex]
Given the roots [tex]\( x = -10 \)[/tex] and [tex]\( x = -6 \)[/tex], we can express the quadratic equation as:
[tex]\[ (x + 10)(x + 6) \][/tex]
To convert this factored form back to the standard quadratic form [tex]\( x^2 + bx + c \)[/tex], expand the factors:
[tex]\[ (x + 10)(x + 6) = x^2 + 6x + 10x + 60 \][/tex]
[tex]\[ = x^2 + 16x + 60 \][/tex]
So the quadratic function that has real zeros at [tex]\( x = -10 \)[/tex] and [tex]\( x = -6 \)[/tex] is:
[tex]\[ f(x) = x^2 + 16x + 60 \][/tex]
Comparing this with the given options, we can see that the correct choice is:
[tex]\[ f(x) = x^2 + 16x + 60 \][/tex]
Therefore, the correct answer is:
[tex]\[ f(x) = x^2 + 16x + 60 \][/tex]
When a quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] has roots [tex]\( \alpha \)[/tex] and [tex]\( \beta \)[/tex], it can be written in the factored form as:
[tex]\[ a (x - \alpha) (x - \beta) = 0 \][/tex]
Given the roots [tex]\( x = -10 \)[/tex] and [tex]\( x = -6 \)[/tex], we can express the quadratic equation as:
[tex]\[ (x + 10)(x + 6) \][/tex]
To convert this factored form back to the standard quadratic form [tex]\( x^2 + bx + c \)[/tex], expand the factors:
[tex]\[ (x + 10)(x + 6) = x^2 + 6x + 10x + 60 \][/tex]
[tex]\[ = x^2 + 16x + 60 \][/tex]
So the quadratic function that has real zeros at [tex]\( x = -10 \)[/tex] and [tex]\( x = -6 \)[/tex] is:
[tex]\[ f(x) = x^2 + 16x + 60 \][/tex]
Comparing this with the given options, we can see that the correct choice is:
[tex]\[ f(x) = x^2 + 16x + 60 \][/tex]
Therefore, the correct answer is:
[tex]\[ f(x) = x^2 + 16x + 60 \][/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.