1) Answer
One set = (7, 6)
Second set = (-6, - 7)
Step by step explanation
Let "x" be a number.
The other number = x -1
The product of the two number is 42
Therefore, x(x -1) = 42
x^2 - x = 42
x^2 - x - 42 = 0
Now we have to factorize the equation.
(x - 7)(x + 6) =0
x = 7 and x = -6
Take x =7, and the other number = x -1
The number is = 7 - 1 = 6
One set of number is (7, 6)
The other set is when x = -6
The other number is = x -1
= -6 -1
= -7
The other set is (-6, -7)
2) Answer
a) x^3 - 49x + 120 = 0
Step by step explanation
Here the solution are 5, 3 and -8
Therefore, the factors are (x - 5)(x - 3) and (x + 8)
Multiplying the factors we get the equation.
(x - 5)(x - 3) (x + 8 ) = 0
(x^2 -5x -3x + 15)(x + 8) = 0
(x^2 - 8x + 15)(x + 8) = 0
x^3 - 8x^2 + 15x + 8x^2 - 64x + 120 = 0
x^3 - 49x + 120 = 0
