anonymous
  • anonymous
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Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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BraydonLevi99
  • BraydonLevi99
What is your question?
anonymous
  • anonymous
@ganeshie8
anonymous
  • anonymous
@dan815

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anonymous
  • anonymous
help
ganeshie8
  • ganeshie8
\(4+5x-6x^2 = (-43/4)H_1+5H_2 +(19/4)H_3\)
anonymous
  • anonymous
ok so we equate them and thats it?
ganeshie8
  • ganeshie8
that is the linear combination
ganeshie8
  • ganeshie8
read the question again
ganeshie8
  • ganeshie8
you want to check if there exist numbers \(a,b,c\) such that : \(4+5x-6x^2 = a*H_1+b*H_2 +c*H_3\)
ganeshie8
  • ganeshie8
plugin the given polynomials for \(H_1, H_2, H_3\) above and get : \(4+5x-6x^2 = a*x^2+b*(x-3) +c*(x^2+4)\)
ganeshie8
  • ganeshie8
compare coefficients both sides
ganeshie8
  • ganeshie8
maybe start by comparing \(x\) coefficient both sides
ganeshie8
  • ganeshie8
Look at below equation \(4+5x-6x^2 = a*x^2+b*(x-3) +c*(x^2+4)\)
ganeshie8
  • ganeshie8
whats the coefficient of x on left hand side ?
ganeshie8
  • ganeshie8
whats the coefficient of x on right hand side ?
ganeshie8
  • ganeshie8
Yes, the coefficients must be equal both sides, therefore \(b=5\)
ganeshie8
  • ganeshie8
next compare constant terms both sides and try finding another variable
ganeshie8
  • ganeshie8
whats the constant term on left hand side ?
anonymous
  • anonymous
4
ganeshie8
  • ganeshie8
what about right hand side ?
anonymous
  • anonymous
c4
ganeshie8
  • ganeshie8
nope, try again
anonymous
  • anonymous
-3b+c4?
ganeshie8
  • ganeshie8
Yes, the constant terms must be equal on both sides : 4 = -3b + 4c
ganeshie8
  • ganeshie8
plugin the value of \(b\) and solve \(c\)
anonymous
  • anonymous
4=-3(5)+4c , 19=4c , 19/4=c
ganeshie8
  • ganeshie8
Yes, compare x^2 coefficients both sides and try finding the value of \(a\) too
ganeshie8
  • ganeshie8
i got a = -43/4
ganeshie8
  • ganeshie8
please double check ur work
ganeshie8
  • ganeshie8
http://www.wolframalpha.com/input/?i=simplify+-43%2F4x%5E2+%2B+5%28x-3%29+%2B+19%2F4%28x%5E2%2B4%29+

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