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23 Aug 2022, 20:31
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Difficulty:
95%
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Question Stats:
25% (02:36) correct
75%
(02:36)
wrong
based on 16
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How many values of z will satisfy the equation |-5z + 8| = |3z +16|?
A. 0
B. 2
C. 3
D. 5
E. 7
(adapted from gmatfree)
A. 0
B. 2
C. 3
D. 5
E. 7
(adapted from gmatfree)
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23 Aug 2022, 22:31
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pintukr
How many values of z will satisfy the equation |-5z + 8| = |3z +16|?
A. 0
B. 2
C. 3
D. 5
E. 7
(adapted from gmatfree)
Solution: A. 0
B. 2
C. 3
D. 5
E. 7
(adapted from gmatfree)
We have \(|-5z + 8| = |3z +16|\)
whenever we have modulus on both sides, it is best to square both the sides
\(|-5z + 8|^2 = |3z +16|^2 \)
\(⇒(-5z+8)^2=(3z+16)^2\)
\(⇒25z^2+64-80z=9z^2+256+96z\)
\(⇒16z^2-176z-192=0\)
\(⇒z^2-11z-12=0\)
It can very well be inferred from here that z will have 2 values and those are 12 and -1 because the sum of the roots of the above quadratic equation is -(-11) = 11 and the product of roots is -12
However, for the sake of clarity lets solve it
\(⇒z^2-12z+z-12=0\)
\(⇒z(z-12)+1(z-12)=0\)
\(⇒(z-12)(z+1)=0\)
This means z = 12 and -1
Hence the right answer is Option B
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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