guys can you plzzzzzzzzzzzz help me on the zero product property in math. i dont undrestand it.?

Question

How can i use the Zero Product Property to help me solve the quadratic equation y=2x^2+5x-12?? plz help im all confused n stressed out

is there a product that equals zero????If not how can i rewrite the quadratic expression as a product????

Answer 1

Note that you can factor this into
y = (2x - 3)(x + 4)
You know that if the product of two numbers is zero, then one of the factors must be zero. So if you were trying to solve (2x - 3)(x + 4) = 0, you'd know that either 2x-3 or x+4 are zero. This means x = 3/2 or -4.

Answer 2

You have to subtract the 7x + 2 from both sides so that there is a zero on the right: 15x^2 - 7x - 2 = 0 Now factor the left-hand side, which isn't easy: (5x + 1)(3x - 2) = 0 Now set each factor separately equal to 0: 5x + 1 = 0 ==> 5x = -1 ==> x = -1/5 and 3x - 2 = 0 ==> 3x = 2 ==> x = 2/3 The point of the "zero product property" is this: If you multiply two quantities together (such as 5x + 1 and 3x - 2), and the answer is zero, then one of the quantities that you multiplied must have been zero. The very important point here is that that's NOT true for any other number. If you multiply two numbers together and get 10, for example, then either number could be anything. One number could be -5 and the other -2; one number could be 77 and the other 10/77, etc. That's why you have to subtract the 7x + 2 from both sides at the beginning of the problem. You need to have a zero on one side, otherwise the whole idea doesn't work.

Answer 3

You are right, you need to write it as a product that equals zero. replace y with zero and FOIL the rest: (2x - 3)(x + 4)

Now it's a product and the zero product property says that if either factor = 0, the whole thing = 0.

So solve the two simpler equations

2x - 3 = 0

or

x + 4 = 0

[Note: actually you had a quadratic function not an equation, and found its zeros, not solved it, but I'm just being picky.]

Answer 4

The zero produt property simply sstaes that if ab=0, then either a= 0 or b= 0.
So if you have factored a quadratic equation to something like the following: (x-5)(x+4)=0, the property states that either x-5=0 or x+4=0.
This lets you set x-5 = 0 getting x = 5 and setting x+4 = 0 getting x = -4.

Answer 5

if a b c = 0 then one or more of a, b, c is zero.

y = (2x^2+5x-12) = (2x-3 ) (x+4)
if y = 0 (this is the definition of a root)
then either 2x-3 = 0 [ x=3/2 ] or x+4 = 0 [ x = -4 ]

so we can use the zero property to find the zeros of the polynomial.

Answer 6

Zero property is when you factor it and then solve it for x setting one of the binomials to equal to 0.

2x^2+5x-12=0
(2x - 3)(x + 4)

(x + 4)=0 so x= -4
(2x - 3)=0 so x = 3/2

Answer 7

You need to change "2x^2+5x-12" into a product.

The basic idea is that ( _x + _) * ( _x +_)

To figure this out:
The two numbers next to x must multiply to 2, since this is your x squared value.

The last two numbers must multiply to -12. (either 6 and 2, 3 and 4 or 12 and 1) . One of the numbers must be negative. Keep guessing till the whole thing multiplies out right.

Then you set each (_x+_) = 0 and solve for x.

Answer 8

what the zero product property means, is if you have two things multiplied together that give you zero, then one or both have to be zero. With a trinomial we factor it into two binomials

(2x-3)(x+4)=0
so we have two binomials multiplied together that give us zero, so set each = 0
2x-3 =0 and x+4=0
2x=3 x=-4
x=3/2

Answer 9

2x² + 5x - 12 = 0
(2x - 3)(x + 4) = 0

2x - 3 = 0
x = 3/2

x + 4 = 0
x = -4

Answer 10

(2x-3)(x+4)=0

2x-3=0 x+4=0

2x=3 x=-4

x=3/2 x= -4