Question

find the quadratic equation whose roots are 3/2 and5/2? is there anyoe who could please help me?

Answer 1

(x - 3/2)(x - 5/2)

Answer 2

do you follow?

you can expand it to get it in standard form

Answer 3

i understand so far

Answer 4

A root is just what makes the equation zero

so you just need to make an equation where the equation is rendered zero when you input those variables as x

Answer 5

If you have an equation whose roots are \(r_1, r_2, r_3, ...\) it can always be written as \((x-r_1)(x-r_2)(x-r_3)....\)

Just multiply it out.

Answer 6

its pretty evident how to do it once you see it

Answer 7

yes

Answer 8

actually, it should be \(k(x-r_1)(x-r_2)...\) as the multiplication by a constant value \(k\) does not affect the roots.

Answer 9

??

Answer 10

you start with
(x - 3/2)(x - 5/2) =0

but you will get ugly fractions that way.

if you multiply both by 2:

2(x-3/2) * 2 * (x- 5/2)
(2x -3) * (2x-5)
now multiply it out

Answer 11

so it will be 2x^2 -6x-15??

Answer 12

Use FOIL to multiply it out. F (first), Outer, Inner, Last

Answer 13

(2x -3) (2x-5)

the "First terms" are 2x and 2x. what is 2x*2x ?

Answer 14

4x right?

Answer 15

when you multiply 2*x*2*x you can change the order of the multiplies, so for example,
2*2*x*x

Answer 16

2*2 is 4 but x*x is not just x

Answer 17

4x^2

Answer 18

yes, the answer is 2*2*x*x, but people simplify it to 4*x*x
and then they use the "short-hand" x^2 for x*x (just to make it look easier)

so you have 4x^2
next, do Outer the outer terms are the very first term and the very last term in
(2x -3) (2x-5)

^ ^

Answer 19

would it be -10x 0r just 10 x

Answer 20

it is 2x* -5 = -10x (the minus sign "sticks" to the number or letter)

to remember this, always use addition, and write (2x - 5) as (2x + -5)
now it is more clear you should use -5

Answer 21

next do Inner
(2x -3) (2x-5)
^ ^

Answer 22

-6x

Answer 23

next, Last
(2x -3) (2x-5)
^ ^

Answer 24

15

Answer 25

so we have 4 products:
4x^2 -10x -6x + 15

you can combine the x terms (the 2 middle terms)

think of it as -10 x's - 6 x's (confusing with the minus signs)
but you get -16 x

Answer 26

so it will be 4x^2- 16x+15?

Answer 27

the answer is
y = 4x^2 -16x + 15

as a check, see
http://www.wolframalpha.com/input/?i=solve+0+%3D+4x%5E2+-16x+%2B+15

Answer 28

thank you sooooo muc