Answer:
The two consecutive integers whose product is 42 are 6 and 7.
Step-by-step explanation:
Let us define first the word "integers" and "consecutive numbers".
Integers
Integers are numbers with no fractional part or no decimals. Integers include all the counting numbers, positive or negative and zero.
Examples: -16, -7, 0, 3, 128
Consecutive Numbers
These are the numbers which follow each other in order, without gaps, from smallest to largest.
Examples: 12 and 13, 21 and 22, 89 and 90
Now, going back to the problem above, let us find the two consecutive integers whose product is 42.
Let x be the first integer.
x + 1 for the second integer. Plus 1 because the next number is 1 more than the first.
Equation:
(x) (x + 1) = 42
We are talking about the product, so we need to multiply the integers.
Solution:
(x) (x + 1) = 42
x² + x = 42
x² + x - 42 = 0
x² + x - 42 = 0 is now a quadratic equation. To continue solving, we need to give the factors of this quadratic equation.
Factors of 42:
First set of factors is 6 and 7.
Second set of factors is -6 and -7.
To factor the quadratic equation, we need to get one positive and one negative.
x² + x - 42
(x + 7) (x - 6)
x = -7 x = 6
Since the answer is a positive integer, throw out -7 answer.
The first integer is 6.
Second Integer = x + 1
= 6 + 1
= 7
The second integer is 7.
Final Answer:
The two consecutive integers whose product is 42 is 6 and 7.
For more examples of finding two consecutive integers, visit the links.
https://brainly.ph/question/1706995
https://brainly.ph/question/1148153
https://brainly.ph/question/69581
Quadratic Equation
The name Quadratic comes from "quad" meaning square, because the variable gets squared like x².
The Standard Form of a Quadratic Equation looks like this:
Quadratic Equation: ax² + bx + c = 0
a, b and c are known values. a can't be 0.
"x" is the variable or unknown value.
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