Question

Help

Answer 1

What is your question?

Answer 2

@ganeshie8

Answer 3

@dan815

Answer 4

help

Answer 5

\(4+5x-6x^2 = (-43/4)H_1+5H_2 +(19/4)H_3\)

Answer 6

ok so we equate them and thats it?

Answer 7

that is the linear combination

Answer 8

read the question again

Answer 9

you want to check if there exist numbers \(a,b,c\) such that :

\(4+5x-6x^2 = a*H_1+b*H_2 +c*H_3\)

Answer 10

plugin the given polynomials for \(H_1, H_2, H_3\) above and get :

\(4+5x-6x^2 = a*x^2+b*(x-3) +c*(x^2+4)\)

Answer 11

compare coefficients both sides

Answer 12

maybe start by comparing \(x\) coefficient both sides

Answer 13

Look at below equation

\(4+5x-6x^2 = a*x^2+b*(x-3) +c*(x^2+4)\)

Answer 14

whats the coefficient of x on left hand side ?

Answer 15

whats the coefficient of x on right hand side ?

Answer 16

Yes, the coefficients must be equal both sides, therefore \(b=5\)

Answer 17

next compare constant terms both sides and try finding another variable

Answer 18

whats the constant term on left hand side ?

Answer 19

4

Answer 20

what about right hand side ?

Answer 21

c4

Answer 22

nope, try again

Answer 23

-3b+c4?

Answer 24

Yes, the constant terms must be equal on both sides :

4 = -3b + 4c

Answer 25

plugin the value of \(b\) and solve \(c\)

Answer 26

4=-3(5)+4c , 19=4c , 19/4=c

Answer 27

Yes, compare x^2 coefficients both sides and try finding the value of \(a\) too

Answer 28

i got a = -43/4

Answer 29

please double check ur work

Answer 30

http://www.wolframalpha.com/input/?i=simplify+-43%2F4x%5E2+%2B+5%28x-3%29+%2B+19%2F4%28x%5E2%2B4%29+