True or Flase?

Question

If solutions of an equation are -5 and 3, the equation could have been x^2-2x-15=0.
Is this true? Please explain it to me to help me understand it better.

Answer 1

It is false, and you can see this by factoring.

To factor the equation, you need to consider all of the factors of the first term and the third term. The first term is easy. It is 1 and 1. The third term, you have 1 and 15 or 3 and 5. Through experience, you'll know to dismiss 1 and 15. Since the third term is negative, you know that you're going to subtract one factor from another. This gives you the second term. 15 - 1 and 1 - 15 won't give you -2. However, 3 - 5 does.

Since your factors are 3 and 5, you need to place the signs. The third number being negative means that you have two different signs. Through trial and error, you will see that:
x^2 - 2x - 15 = 0 gives you
(x - 5)(x + 3) = 0

Now you can find the solutions of the equations. You know that if a*b = 0 then either a = 0 or b = 0. In this case, you know that either x - 5 = 0 or that x + 3 = 0. To get that, x must equal either 5 or -3. These are not the numbers that you have. So the statement is false.

You can work backwards on this. You know the solutions are -5 and 3. You can use this to create your equation of:
(x + 5)(x - 3) = 0 <== Multiply this out to get:
x^2 + 2x - 15 = 0

Answer 2

the solutions for the equation x^2 - 2x - 15 are 5 and -3 !
so that statement is false !

now to find the equation whose roots are -5 and 3 u just need to solve an equation (x + 5)(x - 3)
Note that i changed the negative to positve and vice versa!
so expanding this u get : x^2 + 2x - 15 !
[ x^2 + 5x - 3x - 15]

Answer 3

No. Had to be (x+5)(x-3)=x^2+2x-15=0
either (x+5) =0 or (x-3)=0 makes product zero.

Your x^2-2x-15 = (x-5)(x+3)=0 gives
x=5 and x=-3

Answer 4

we use zero product property to solve quadratic equations which means that each factor is set to zero. so, if your assumption were to be true, when we factor x^2 - 2x - 15, we have (x - 5)(x + 3) or x -5 =0 and x + 3 = 0. thus we would have x = 5 and x = -3.
in order to find the equation whose solutions are given, change the signs of solutions and add them to x
y = (x + 5)(x - 3) or y = x^2 + 2x - 15

Answer 5

x² - 2x - 15 = 0

the middle term is - 2x

find the sum of the middle term

x = 1

multiply the first term 1 times the last term 15 equals 15 and facto

factors of 15 are

1 x 15
3 x 5. . .<=. .use there factors

- 5 and + 3 satisfy the sum of the middle term

insert - 5x + 3x into the equation

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

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

(x + 3)(x - 5)

- - - - - - - -

Roots

x + 3 = 0

x + 3 - 3 = 0 - 3

x = - 3

- - - - - -

Roots

x - 5 = 0

x - 5 + 5 = 0 + 5

x = 5

- - - - - - - -s-

Answer 6

(An equation whose first coefficient is 1) is this way:

x^2 - sx + p = 0

Where s is the sum of the roots and p is their product

So:

s = -5 + 3 = -2
(So - s = 2)

and

p = (-5)*3= -15

Hence, an equation whose roots are -5 and 3 are

x^2 +2x - 15 = 0

Ilusion

Answer 7

it false,

if you sustitute 3 in the equation then you have: 9-6-15 = -12
if you sustitute -5 in the equation then you have: 25+10-15=20


The solutions of this equations are 5 and -3

You can see it replacing these numbers in the equation

Answer 8

100% False

Goodluck! ♥Melissa♥

Answer 9

yes

Answer 10

it false