Create an equation that has solutions 1 and -1. Leave your equation in factored form!

Mathematics

2 answers:

choli [55]3 years ago

8 0

Answer:

(x-1)(x+1)=0

Step-by-step explanation:

WINSTONCH [101]3 years ago

3 0

If the factors are a and b then we can create the equation as :

$(x-a)(x-b)=0$

Here we are given the solutions as 1 and -1.

Let us plug them in the above equation and try to make an equation using it.

let a=1 and b=-1

So we have,

$(x-1)(x-(-1))=0$

Simplifying,

$(x-1)(x+1)=0$

Answer:

The equation with solutions 1 and -1 is:

$(x-1)(x+1)=0$

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The height of a triangle is 3cm less than twice the base. The area is 10cm2

Kamila [148]

Answer:

The base is 4cm and the height is 5cm.

Step-by-step explanation:

This is a solve the system question. Call H the height of the triangle and B the base. The question tells us:

$H=2B-3$

and

$\frac{B \times H}{2}=10$

Sub the first equation into the second (as H is already isolated). You will end up with a quadratic equation - solve that any way you wish (e.g. quadratic formula). I've provided the factored form below which shows you the roots:

$\frac{B(2B-3)}{2}=10\\\frac{2B^2-3B}{2}=10\\2B^2-3B=20\\2B^2-3B-20=0\\(2B+5)(B-4)=0\\B= - \frac{5}{2},4$

In this question, we take B=4. You can't have a negative side length so the other answer is eliminated. Now sub the value for B into either of the original equations. I'll use the first, again because H is already isolated:

$H=2(4)-3\\H=8-3\\H=5$