Solve this quadratic equation step by step 3t²-12t=0 , Answer should be t=0 and t=4
Answers
Answer:
Step by step solution :
STEP
1
:
Equation at the end of step 1
(3t2 - 12t) - 3 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
3t2 - 12t - 3 = 3 • (t2 - 4t - 1)
Trying to factor by splitting the middle term
3.2 Factoring t2 - 4t - 1
The first term is, t2 its coefficient is 1 .
The middle term is, -4t its coefficient is -4 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 1 • -1 = -1
Step-2 : Find two factors of -1 whose sum equals the coefficient of the middle term, which is -4 .
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Step-by-step explanation:
Given :-
3t²-12t = 0
To find :-
Solve the quardratic equation ?
Solution :-
Factorization method:-
Given that 3t²-12t = 0
=> 3t(t-4) = 0
=> 3t = 0 or t-4 = 0
=> t = 0/3 or t = 0+4
=> t = 0 or t = 4
Completing the square method:-
Given that 3t²-12t = 0
On dividing by 3 both sides then
=> (3t²/3)-(12t/3) = 0/3
=> t²-4t = 0
=> t²-2(t)(2) = 0
On adding 2² both sides then
=> t²-2(t)(2)+2² = 0+2²
=> (t-2)² = 4
=> t-2 = ±√4
=> t-2 = ±2
=> t = 2±2
=> t = 2+2 or 2-2
=> t = 4 or 0
Formula method :-
We know that
x = [-b±√(b2-4ac)]/2a
We have ,
In 3t²-12t = 0,
a = 3
b = -12
c = 0
On Substituting these values in the above formula then
=> t = [ -(-12)±√{(-12)²-4(3)(0)}]/2(3)
=> t = [12±√(144-0)]/6
=> t = (12±√144)/6
=> t = (12±12)/6
=> t = 6(2±2)/6
=> t = 2±2
=> t = 2+2 or 2-2
=> t = 4 or 0
Answer :-
The solutions of the quardratic equation 3t²-12t=0 are 0 and 4
Used Methods:-
→ Factorization method
→ Completing the square method
→ Formula method