Use factoring and the zero-product property to solve the following problems.
2 answers:
Answer:
see explanation
Step-by-step explanation:
Divide through by 2
2a² - 5a + 3 = 0
To factor the quadratic
Consider the factors of the product of the coefficient of the a² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 3 = 6 and sum = - 5
The factors are - 2 and - 3
Use the factors to split the a- term
2a² - 2a - 3a + 3 = 0 ( factor the first/second and third/fourth terms )
2a(a - 1) - 3(a - 1) = 0 ← factor out (a - 1)
(a - 1)(2a - 3) = 0
Equate each factor to zero and solve for a
a - 1 = 0 ⇒ a = 1
2a - 3 = 0 ⇒ 2a = 3 ⇒ a =
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Answer:
Second option:
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
We know that a line goes through the points and
Since the line intersects the y-axis when , then the y-intercept of this line is:
Substitute the y-intercept and coordinates of the point into the equation
and solve for "m":
By definition, the slopes of parallel lines are equal, then the slope of the other line is:
Knowing that it passes through the point , we can substitute values into the equation
and solve for "b":
Therefoe, the equation of this line is: