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What is the sum of all values of that satisfy the equation 4

Expert replies
by BTGmoderatorDC » Sat Mar 16, 2019 7:36 pm

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Answers

A

B

C

D

E

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Difficulty

What is the sum of all values of that satisfy the equation 4x^2 +16=32x?

A) −8
B) −4√2
C) −4
D) 4√2
E) 8

OA E

Source: Veritas Prep
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Source: — Problem Solving |

by GMATGuruNY » Sun Mar 17, 2019 2:55 am
BTGmoderatorDC wrote:What is the sum of all values of that satisfy the equation 4x^2 +16=32x?

A) −8
B) −4√2
C) −4
D) 4√2
E) 8
For any quadratic in the form x² + bx + c = 0:
Product of the roots = c
Sum of the roots = -b

Given equation:
4x² + 16 = 32x
4x² - 32x + 16 = 0
x² - 8x + 4 = 0

In the resulting quadratic, b=-8.
Thus:
Sum of the roots = -(-8) = 8.

The correct answer is E.
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