quadratic Equations

Question

One of the roots of the equation 5x2−12x+c=0 is three times as big as the other root. Find the value of c.

One of the roots of the equation 5x²−12x+c=0 is three times as big as the other root. Find the value of c.

Answer 1

Using the quadratic equation, the two roots are 12 + (144-4(5)c)^1/2 and 12- (144-4(5)c)^1/2 

                                                                         10                                10

Set the larger root equal to 3 times the smaller root and solve for c.

 

12 + (144-20c)^1/2 =  3(12 - (144-20c)^1/2

     10                              10

 

12 + (144-20c)^1/2 = 36 - 3(144-20c)^1/2

 

4(144-20c)^1/2 = 36-12 = 24     (divide both sides by 4)

 

(144 - 20c)^1/2 =  6   (square both sides)

 

144-20c = 36

 

20c = 144-36 = 108

 

c = 5.4

 

The roots are 9/5  and 3/5