Help on quadratic equation

Phaedrus

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Mar 12, 2019
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Give that m is one of the roots of the quadratic equation x²+5x-12=0
Show that m³=37m-60.
 

Dr.Peterson

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Give that m is one of the roots of the quadratic equation x²+5x-12=0
Show that m³=37m-60.
The fact that m is a root means that m²+5m-12=0. You want to show that m³-37m+60=0. This suggests that the former polynomial might be a factor of the latter. Is it?
 

mmm4444bot

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Jomo

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You can always find the value(s) for m and see if m³=37m-60 although there are easier ways.
 

MarkFL

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One way to approach this is to write:

\(\displaystyle m^3-37m+60=(m+a)(m^2+5m-12)\)

Expand the RHS and collect like terms:

\(\displaystyle m^3-37m+60=m^3+(a+5)m^2-(12-5a)m-12a\)

What does the comparison of corresponding coefficients tell you about \(a\)?
 
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