Help on quadratic equation

[Phaedrus]

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

 

[Dr.Peterson]

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]

Hello. Please read the forum's submission guidelines. Thank you!

?

 

[Steven G]

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

 

[MarkFL]

One way to approach this is to write:

[MATH]m^3-37m+60=(m+a)(m^2+5m-12)[/MATH]
Expand the RHS and collect like terms:

[MATH]m^3-37m+60=m^3+(a+5)m^2-(12-5a)m-12a[/MATH]
What does the comparison of corresponding coefficients tell you about \(a\)?