Respuesta :
The factors of given equation are -3/4 and -2.
Rewriting the equation -
4x² + 11x + 6 = 0
The factors for the given expression will be calculated based on two factors -
1. The sum of factors should be equal to sum of numeral value of b (11 in this case)
2. The product of factors should be equal to product of numeral values of a and c (24 in this case)
As per the above rules, the appropriate factors should be 8 and 3.
Rewriting the given equation with possible factors -
4x² + 8x + 3x + 6 = 0
Taking common values
4x(x + 2) +3(x + 2) = 0
(x + 2) (4x + 3) = 0
x = -3/4, -2
Thus, the factors of given expression are -3/4 and -2.
To check the correctness of factors, we will keep each value of x in equation.
When x = -3/4
4x² + 11x + 6 = 0
4(-3/4) + 11(-3/4) + 6 = 0
9/4 -33/4 + 6 = 0
9/4 = 2.25 and 33/4 = 8.25
2.25 - 8.25 + 6 = 0
-6 + 6 = 0
0 = 0
When x = -2
4x² + 11x + 6 = 0
4(-2)² + 11(-2) + 6 = 0
16 - 22 + 6 = 0
22 - 22 = 0
0 = 0
Since both values of x give 0 on both sides of equation, the factors of equation are correct.
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