Solve the maths equation: z^2 - 9z + 8 = 0?

Question

Z=

(3 marks)

this is from my revision paper, please can you show me how to work it out.

Answer 1

z² - 9z + 8 = 0

The middle term is - 9x

the first term z² = 1

multiply the first term 1 times the last term 8 equals 8 and factor

Factors of 8

1 x 8. . .<=. .use these factors
2 x 4

- 8 and - 1 satisfy the sum of the middle term

- 1 = - z

insert - 8x and - z into the equation

z² - 9z + 8 = 0

Group factor

z² - 8z - z + 8 = 0

z(z - 8) - 1(z - 8) = 0

(z - 1)(z - 8) = 0

- - - - - - - -

Roots

z - 1 = 0

z - 1 + 1 = 0 + 1

z = 1

- - - - - - - - -

Roots

z - 8 = 0

z - 8 + 8 = 0 + 8

z = 8

- - - - - - - s-

Answer 2

Remember PEMDAS. This is key in figuring out how to simplify equations... (and also remembering that you can only combine like numbers (numbers with numbers, variables with variables) Parenthesis Exponents Multiply Divide Add Subtract Question 1: 4x+8=3(x+8) Simplify the parenthesis: 4x+8 = (3*x)+(3*8) 4x+8 = 3x+24 4x = 3x+24-8 (subtract 8 from both sides) 4x = 3x+16 4x - 3x = 16 (subtract 3x from both sides) x = 16 Question 2: 2y+ x/2 = 7 - since this is a linear equation there will be lots of answers. The easiest way to is to make one variable a 0 and solve for the equation. One possible answer would be: 2y + 0 = 7 y = 7/2 y = 3.5 The ordered pair would be (0,3.5) solving it the other way would give an ordered pair of (14,0) Question 3. -9z = 7(3+2w)+ -8w+17z+-11 First thing to do is remove the + sign before the minus signs. (do not do this if you have a +- in front on a pair of parenthesis) -9z = 7(3+2w)-8w+17z-11 -9z = 21+14w-8w+17z-11 (multiple out through the parenthesis) -9z = 21-6w+17z-11 (combine the w variable) 0 = 21-6w+26z-11 (comebine the z variable) 0 = 26z-6w+10 (simplified) 26z-6w = -10 (simplified into an equation) 13z-3w = -5 (divide the entire equation by 2) - Most people will forget this step. Hope this helps.

Answer 3

first of all u know that -8 + 8 = 0. then that means that z^2 - 9z = -8. now u have to figure out the value of z. i used trial-and-error to get z = 8.

8 x 8 = 64, and 9 x 8 = 72. this means that z^2 = 64 and 9z = 72.

Answer 4

z^2 - 9z + 8 = 0
(z - 8)(z - 1) = 0
z - 8 = 0 or z-1 = 0
z = 8 or z = 1

Answer 5

z^2 - 9z + 8 = 0

What are the factors of 8 that add to -9?
Answer: -1 and -8

(z - 8)(z - 1) = 0
z = 8; z = 1

Answer 6

In z^2-9z+8=0, we can factor this.

To factor, you see, what factors of 8 add up to 9?
That is 8 and 1

Then we look at the signs. Its a negative-positive, so the signs would both have to be negative.

So, we get
(z-1)(z-8)=0

then we set each part equal to zero.

so we have
z-1=0 and z-8=0

then we solve for z in both to get

z=1 and z=8, or {1,8}

Answer 7

z^2 - 9z + 8 = 0

transpose 8

z^2 - 9z = -8

factor z out of the equation to get two possible values of z.

z (z-9) = -8

then from this you will know that z = -8 or z - 9 = -8 or z=1

you have to possible solutions being z as -8 or z as 1.

then substitute z from the original equation with both of your possible solutions, then choose the value for z that verifies the equation.

:D

Answer 8

z^2 - 9z + 8 = 0
(z-1)(z-8) = 0
z-1 = 0 or z-8 = 0
z = 1, 8

Answer 9

z^2 - 9z + 8 = 0
(z-8)(z-1)=0
z-8=0 or z-1=0
z=8 or z=1

Answer 10

Find Two numbers that add to make -9, and x to make 8,
-1 and -8
so solution is
(z-1)(z-8)