Answer:
D
Step-by-step explanation:
Given the root of a quadratic equation x = a then the factor is (x - a)
Here the roots are x = 5 and x = 7 , then the corresponding factors are
(x - 5) , (x - 7)
The equation is then the product of the factors, that is
y = (x - 5)(x - 7) ← expand using FOIL
= x² - 7x - 5x + 35 ← collect like terms
y = x² - 12x + 35 → D
The quadratic equation has roots of 5 and 7 so, the quadratic equation would be equal to [tex]y = x^{2} - 12x + 35[/tex].
Suppose that the given quadratic equation is
ax^2 + bx + c = 0
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
It is Given the root of a quadratic equation x = a then the factor is (x - a)
Here the roots are x = 5 and x = 7 , then the other factors are
(x - 5) , (x - 7)
The equation is then the product of the factors,
[tex]y = (x - 5)(x - 7)\\y = x^{2} - 7x - 5x + 35 \\y = x^{2} - 12x + 35[/tex]
Learn more about finding the solutions of a quadratic equation here:
https://brainly.com/question/3358603
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