Pls answer the question attached..
Answers
Answer:
-4/3, 3/4
Step-by-step explanation:
Given Equation is 12x² + 7x - 12 = 0
⇒ 12x² - 9x + 16x - 12 = 0
⇒ 3x(4x - 3) + 4(4x - 3) = 0
⇒ (3x + 4)(4x - 3) = 0
⇒ x = -4/3, 3/4.
Therefore, roots of the equation are : -4/3, 3/4.
Note: Since it was asked for 2 marks, i have solved using factorization method.
Hope it helps!
Solving 12x2+7x-12 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 12
B = 7
C = -12
Accordingly, B2 - 4AC =
49 - (-576) =
625
Applying the quadratic formula :
-7 ± √ 625
x = ——————
24
Can √ 625 be simplified ?
Yes! The prime factorization of 625 is
5•5•5•5
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).
√ 625 = √ 5•5•5•5 =5•5•√ 1 =
± 25 • √ 1 =
± 25
So now we are looking at:
x = ( -7 ± 25) / 24
Two real solutions:
x =(-7+√625)/24=(-7+25)/24= 0.750
or:
x =(-7-√625)/24=(-7-25)/24= -1.333