Question

Determine the coordinates of the x-intercepts for the quadratic equation 5x^2 – 21x + 4 = 0.

Answer 1

Just make the factors of it and then find x..

Answer 2

i dont know how to factor

Answer 3

first you multiply the 5 with 4, so you get 20 and then you have to find two numbers that give you 20 when you multiply them and give you a sum of -21 when you add them

Answer 4

I'll show you an easy example so that you learn how to factorize.
\[2x ^{2}+5x+3\]

Answer 5

2x3=6
and 2+3=5

Answer 6

so you basically split the middle term
into 2x+3x

Answer 7

now you have a new equation that looks like this \[2x ^{2}+2x+3x+3\]

Answer 8

then you factorize like this:
\[2(x+1)+3(x+1) so the (x+1) is common for both of them

Answer 9

i forgot the x after the 2

Answer 10

so it's (2x+3)(x+1)

Answer 11

Do you get it?

Answer 12

you can check if it's right by just expanding the brackets... do you know how to expand?

Answer 13

i still dont get it my teacher is kinda teaching me slowly

Answer 14

okay factorising is when you try to break down the equation to its components

Answer 15

you do that by finding common factors

Answer 16

yeah

Answer 17

you get this?

Answer 18

kinda

Answer 19

so you need to split the middle term(in my example it's the 5x) to split it means that you have to first multiply the number in front of the x^2 with the last number and then you find a number that will give you the 5 in the middle when you add them and the number you got when you multiplied

Answer 20

like my example it was 2 and 3... because 2+3=5

Answer 21

and 2*3=6

Answer 22

with me?

Answer 23

yea im with you

Answer 24

do you get how we split the middle term

Answer 25

yeah it mean you first muilitply the number in front of x^2

Answer 26

with the last number which is 3 here

Answer 27

so you get 6

Answer 28

you example or my example?

Answer 29

well my example is easier to understand if you haven't done this before

Answer 30

and it's much easier if your teacher explains it to you right in front of you so you can see it step by step

Answer 31

yeah i know, can we use my example?