5tsquare -8t-12=0 by the factorise method
Answers
Step-by-step explanation:
Solving 5t2-8t-12 = 0 by the Quadratic Formula .
According to the Quadratic Formula, t ,the solution for At2+Bt+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
t = ————————
2A
In our case, A = 5
B = -8
C = -12
Accordingly, B2 - 4AC =
64 - (-240) =
304
Applying the quadratic formula :
8 ± √ 304
t = —————
10
Can √ 304 be simplified ?
Yes! The prime factorization of 304 is
2•2•2•2•19
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 304 = √ 2•2•2•2•19 =2•2•√ 19 =
± 4 • √ 19
√ 19 , rounded to 4 decimal digits, is 4.3589
So now we are looking at:
t = ( 8 ± 4 • 4.359 ) / 10
Two real solutions:
t =(8+√304)/10=(4+2√ 19 )/5= 2.544
or:
t =(8-√304)/10=(4-2√ 19 )/5= -0.944
Two solutions were found :
t =(8-√304)/10=(4-2√ 19 )/5= -0.944
t =(8+√304)/10=(4+2√ 19 )/5= 2.544