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38. Which quadratic equation has roots of 5 and 7?

A. [tex]y = x^2 + 2x - 35[/tex]
B. [tex]y = x^2 - 2x - 35[/tex]
C. [tex]y = x^2 + 12x + 35[/tex]
D. [tex]y = x^2 - 12x + 35[/tex]

Select one:
a. A
b. B
c. C
d. D

Sagot :

GinnyAnsweridn
To find the quadratic equation with roots 5 and 7, we need to use the fact that if a quadratic equation has roots [tex]\(a\)[/tex] and [tex]\(b\)[/tex], it can be expressed as:

[tex]\[ (x - a)(x - b) = 0 \][/tex]

Given that the roots are 5 and 7, we start by writing:

[tex]\[ (x - 5)(x - 7) = 0 \][/tex]

Next, we expand this expression:

[tex]\[ (x - 5)(x - 7) \][/tex]
[tex]\[ = x(x - 7) - 5(x - 7) \][/tex]
[tex]\[ = x^2 - 7x - 5x + 35 \][/tex]
[tex]\[ = x^2 - 12x + 35 \][/tex]

Therefore, the quadratic equation with roots 5 and 7 is:

[tex]\[ y = x^2 - 12x + 35 \][/tex]

Looking at the given options, we see that this matches option J.

So, the correct answer is:

d. J
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