The factors of equation are -4 and -5.
Rewriting the equation -
x² + 9x + 20 = 0
ax² + bx + c = 0
The mentioned equation will be factorized using the given two rules -
1. sum of the factors will be equal to numeral in middle expression b (9x in this case)
2. product of factors will be equal to product of a and c (20 in this case)
Using above rules, the appropriate factors should be 5 and 4.
Representing the factors in mentioned equation -
x² + 4x + 5x + 20 = 0
Taking common factors
x(x + 4) +5(x + 4) = 0
(x + 4) (x + 5) = 0
x = -4, -5
Hence, the two factors of given equation are -4 and -5.
To check the answer, we will keep each value of x in the equation -
When x = -4
x² + 9x + 20 = 0
(-4)² + 9(-4) + 20 = 0
16 -36 + 20 = 0
36 - 36 = 0
0 = 0
When x = -5
x² + 9x + 20 = 0
(-5)² + 9(-5) + 20 = 0
25 - 45 + 20 = 0
45 - 45 = 0
0 = 0
As both Left Hand Side and Right Hand Side of the equation are same for both values of x, the factors are correct.
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