Decide equation using only factors to solve this problem 12x^{2} + 5x - 2 = 0

Emeli Hagan 2021-03-09 Answered
Decide equation using only factors to solve this problem
12x2 + 5x  2=0
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Expert Answer

grbavit
Answered 2021-03-10 Author has 109 answers

In order to factor the quadratic, we need to find the values of a, b and c for the given quadratic 12x2 + 5x  2=0 on comparing with standard quadratic
ax2 + bx + c=0
12x2 + 5x  2=0
a=12b=5, c= 2.
Now, let us apply ac method to factor the quadratic.
We got ac= 24 and b=5. So, we need to find the factors of -24, those add upto 5.
ac=12 2= 24(Product)
b=5(Sum)
-24 could be factored in two numbers 8 and -3 that add upto 5.
Therefore, middle term 5x of expression 12x2 + 5x  2=0, could be break into two terms 8x and -3x.
Then we need to make the break the expression into groups.
Factor out 3x form 12x2  3x and factor out 2 from:
8x  2.
Then factor out common parenthesis (4x  1).
We got factored form (4x  1)(3x + 2)=0
12x2 + 5x  2=0
(12x2  3x) + (8x  2)=0
3x(4x  1) + 2(4x  1)=0
Factor out common parenthesis (4x  1)
(4x  1)(3x + 2)=0
By applying zero product rule, we need to set each factor equal to zero and solve for x.
We got x=14, 23.
4x  1=0 or 3x + 2=0
+1+122
4x4=14 or 3x3=23
x=1.4 or x=23

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