Problem Solving (PS) | Re: How many values of z will satisfy the equation

Solution:

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
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