# Help on quadratic equation

#### Phaedrus

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

#### Dr.Peterson

##### Elite Member
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?

• topsquark

#### mmm4444bot

##### Super Moderator
Staff member
Hello. Please read the forum's submission guidelines. Thank you! #### Jomo

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

#### MarkFL

##### Super Moderator
Staff member
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 $$a$$?