Question

find all the real values of x which satisfy x^2-3x+2>0 and x^2-3x-4<= 0
(now both the inequalities will give different solutions, will the solution of one has to satisfy the other inequality, pls explain)

Answer 1

did you solve \(x^2-3x+2>0\) ?

Answer 2

the key word in the question
"find all the real values of x which satisfy \(x^2-3x+2>0\) AND \( x^2-3x-4\leq 0\)"
is AND
solve each separately and take the intersection of the two sets

Answer 3

now the question is, do you know the solution to \(x^2-3x+2>0\) ?

Answer 4

yes i did manage to factorize both x^2−3x+2=0 AND x^2−3x−4=0 .. the insertion part I am not getting.

Answer 5

sorry it will be the intersection and not insertion

Answer 6

it is more than just factoring
once you have \(x^2-3x+2=(x-1)(x-2)\) you see that it is positive on the intervals
\[(-\infty,1)\cup (2,\infty)\]

Answer 7

is that part clear?

Answer 8

yes how about the other part and combining both ?

Answer 9

which means 1<x<2 in this interval x^2−3x+2 is positive

Answer 10

and the solution to the next one is \((-1,4)\) if i am not mistaken

Answer 11

oh no

Answer 12

\(y=x^2-3x+2\) is a parabola that opens UP

Answer 13

it is negative between the zeros, positive outside them

Answer 14

in the interval \((1,2)\) it is NEGATIVE
you want positive

Answer 15

ok but how to get a solution that satisfies both ... how to write the answer ?

Answer 16

well we can't hope to get them together until we know what they are separately first !

Answer 17

the solution to the first one is \(x<1\) or \(x>2\)
better written in interval notation as
\[(-\infty,1)\cup (2,\infty)\]

Answer 18

yes i get u

Answer 19

the solution to the second one is \(-1\leq x\leq 4\) which is the same as \[[-1,4]\]

Answer 20

now since you are given an AND statement you need to find the intersection of the two sets; the values of \(x\) that satisfy both

Answer 21

what is in common to both of these sets?
the interval \([-1,1)\) is in both of them for example

Answer 22

so it will be between -1 and 1 and 2 and 4

Answer 23

yes

Answer 24

be careful with the inequalities because one is \(\leq \) and the other is \(<\)

Answer 25

-1<=x<1 and 2<x<= 4 ?

Answer 26

in interval notation the one on the left is \([-1,1)\) or you can write \(-1\leq x<1\)

Answer 27

yes that looks good

Answer 28

although if you are a stickler for details, you should not use the word "and" in your answer

Answer 29

hey many thanks ....u explained it extremely well :) ..

Answer 30

-1<=x<1 OR 2<x<= 4

Answer 31

yw

Answer 32

how do i give a medal ? i am new to open study ?