Use the roots given, and plug them in to a factored form. Then, foil! It can also be helpful to multiply the equation to get rid of decimals/fractions.

(x - 3/4)(x + 5) = 0

x^2 - 3/4x + 5x - 3 3/4 = 0

x^2 + 4.25 - 3.75 = 0 (multiply everything by 4)

4x^2 + 17 - 15 = 0

#2. y = 0, -4

Both 4y^2 and 16y contain a 4 in the coefficient and a y in the variables. Therefore, we can factor out a 4y from each.

4y(y + 4) = 0

Then, set both parts of the factored equation equal to 0.

4y = 0

y = 0

y + 4 = 0

y = -4

#3. a = 0, -3

Both 6a^5 and 18a^4 contain a 6 in the coefficient and an a in the variables. Therefore, we can factor out a 6a^4 from each.

6a^4(a + 3) = 0

Then, set both parts of the factored equation equal to 0.

6a^4 = 0

a = 0

a + 3 = 0

a = -3

#4. x = -8

We are looking for two terms that multiply to equal a * c, and add up to equal b. We know that 8 + 8 = 16, and 8 * 8 = 64. There are no negatives in this equation, therefore both signs in our factored form are positive.

(x + 8)(x + 8) = 0

x + 8 = 0

x = -8

#5. x = -8, 8

First, subtract 64 from both sides. The key word here is 'factoring.' If this was not present, there is a different way (which may be easier for some).

x^2 = 64

x^2 - 64 = 0

Next, use the difference of two squares property to factor (x - c)(x + c), and set the two binomials equal to 0.

(x - 8)(x + 8) = 0

x - 8 = 0

x = 8

x + 8 = 0

x = -8

Hope this helps!! :)

3 0

3 years ago