Factor to find the zeros of the function defined by the quadratic expression. 16x2 − 240x + 896 A) x = 7 or x = 8 B) x = 7 or x = −8 C) x = −7 or x = 8 D) x = −7 or x = −8
Mathematics · Middle School · Tue Nov 03 2020
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Given the quadratic function:
16x^2 - 240x + 896
Determine the zeros of the function.
Solution:
In order to determine the zeros of the function, we must factor it first. Noticed that the given quadratic equation has a common factor of 16, therefore we can factor out 16 and simplify.
16x^2 - 240x + 896 = 0
16(x^2 - 15x + 56) = 0
Now that we have the simplified version, we can directly factor the zeros of the quadratic equation. In order to factor a quadratic equation, we must look for the numbers that when add together, the sum will be the middle value of the quadratic equation, and when multiplied, the product is last value of the quadratic equation.
Those two numbers are - 7 and -8, since when you add them, the sum will be -15, and when multiplied the product will be 56. Negative sign became positive since similar signs will result to a positive value.
16( x - 7) ( x- 8) = 0
Equate each factored number into zero to get the values of x
x - 7 = 0
x = 7
x - 8 = 0
x = 8
The answer to the problem is A) x = 8, or x = 7