math problem please help asap

Question

One of the roots of the equation 5x^2−12x+c=0 is three times as big as the other root. Find the value of c.

Answer 1

Let one root be R and the other be 3R.

 

Root Sum: -b/a = 12/5

 

Root Product: c/a = c/5

 

This means 4R=12/5 so that the roots are 3/5 and 9/5.

 

Finally, c=5(R)(3R)=15R² = 15(3/5)² = 27/5

Answer 2

use the quadratic equation

a=5, b=-12, c=c

[12±√(144-20c)]/10

(12+√[144-20c])/10=3(12-√[144-20c])/10

multiply both sides by 10

12+√(144-20c)=3(12-√[144-20c])

12+√(144-20c)=36-3√(144-20c)

√(144-20c)+3√(144-20c)=36-12

4√(144-20c)=24

√(144-20c)=6

144-20c=36

144-36=20c

108=20c

c=108/20

c=5.4 (answer)

check:

substitute into the quadratic formula

[12±√(144-20*5.4)]/10

[12±√(144-108)]/10

[12±√36]/10

(12±6)/10

18/10=1.8

6/10=0.6

1.8 is 3 times 0.6