- Thread starter Phaedrus
- Start date

- Joined
- Nov 12, 2017

- Messages
- 3,634

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?Give that m is one of the roots of the quadratic equation x²+5x-12=0

Show that m³=37m-60.

- Joined
- Oct 6, 2005

- Messages
- 10,281

- Joined
- Nov 24, 2012

- Messages
- 1,587

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

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 \(a\)?