To identify if any of the values 1, 2, 3, 4, or 5 are zeros of the polynomial, we substitute each value into the equation and check if the equation equals zero.
For x = 1:
(1 - 3)(1 - 4) = (-2)(-3) = 6
Since the equation does not equal zero, 1 is not a zero of the polynomial.
For x = 2:
(2 - 3)(2 - 4) = (-1)(-2) = 2
Since the equation does not equal zero, 2 is not a zero of the polynomial.
For x = 3:
(3 - 3)(3 - 4) = (0)(-1) = 0
Since the equation equals zero, 3 is a zero of the polynomial.
For x = 4:
(4 - 3)(4 - 4) = (1)(0) = 0
Since the equation equals zero, 4 is a zero of the polynomial.
For x = 5:
(5 - 3)(5 - 4) = (2)(1) = 2
Since the equation does not equal zero, 5 is not a zero of the polynomial.
Therefore, the zeros of the polynomial (x - 3)(x - 4) = 0 are x = 3 and x = 4.
Step-by-step explanation:
The equation (x - 3)(x - 4) = 0 has two zeros, which are x = 3 and x = 4. When we substitute these values into the equation, it equals zero. For the other values, the equation does not equal zero, so they are not zeros of the polynomial.
Answers & Comments
Answer:
Equation: (x - 3)(x - 4) = 0
To identify if any of the values 1, 2, 3, 4, or 5 are zeros of the polynomial, we substitute each value into the equation and check if the equation equals zero.
For x = 1:
(1 - 3)(1 - 4) = (-2)(-3) = 6
Since the equation does not equal zero, 1 is not a zero of the polynomial.
For x = 2:
(2 - 3)(2 - 4) = (-1)(-2) = 2
Since the equation does not equal zero, 2 is not a zero of the polynomial.
For x = 3:
(3 - 3)(3 - 4) = (0)(-1) = 0
Since the equation equals zero, 3 is a zero of the polynomial.
For x = 4:
(4 - 3)(4 - 4) = (1)(0) = 0
Since the equation equals zero, 4 is a zero of the polynomial.
For x = 5:
(5 - 3)(5 - 4) = (2)(1) = 2
Since the equation does not equal zero, 5 is not a zero of the polynomial.
Therefore, the zeros of the polynomial (x - 3)(x - 4) = 0 are x = 3 and x = 4.
Step-by-step explanation:
The equation (x - 3)(x - 4) = 0 has two zeros, which are x = 3 and x = 4. When we substitute these values into the equation, it equals zero. For the other values, the equation does not equal zero, so they are not zeros of the polynomial.