Using factoring and zero-product property solve:
4a^2 -10a +6=0
Thank's a lot.
2(2a^2-5a+3)
is
2(2a-3)(a-1)
To solve the quadratic equation 4a^2 - 10a + 6 = 0 using factoring and the zero-product property, follow these steps:
Step 1: Arrange the equation in standard quadratic form, with the terms in descending order:
4a^2 - 10a + 6 = 0
Step 2: Factor the quadratic expression. Consider the factors of the first term (4) and the last term (6) that could add up to the middle term (-10):
The factors of 4 are 1 and 4, and the factors of 6 are 1, 2, 3, and 6.
By trial and error, we find that 2 and 3 satisfy the conditions.
Therefore, we can write the equation as:
(2a - 2)(2a - 3) = 0
Step 3: Apply the zero-product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.
Set each factor in parentheses equal to zero and solve for 'a':
2a - 2 = 0 or 2a - 3 = 0
Solving the first equation:
2a - 2 = 0
Add 2 to both sides:
2a = 2
Divide by 2:
a = 1
Solving the second equation:
2a - 3 = 0
Add 3 to both sides:
2a = 3
Divide by 2:
a = 3/2 or 1.5
So, the solutions to the quadratic equation are:
a = 1 or a = 3/2 (or a = 1.5)
Therefore, the values of 'a' that satisfy the equation 4a^2 - 10a + 6 = 0 are a = 1 and a = 1.5 (or a = 3/2).