Finding \(\displaystyle{3}{r}^{{2}}+{r}{s}-{2}{s}^{{2}}+{2}{r}-{3}{s}\) given that r and s

Saul Cochran

Saul Cochran

Answered question

2022-04-06

Finding 3r2+rs2s2+2r3s given that r and s are the roots of x2+x+7

Answer & Explanation

Wernbergbo9d

Wernbergbo9d

Beginner2022-04-07Added 12 answers

Step 1
1) (x2+x+7)=0
and r,s is roots so rs=7, r+s=1 this implies s=(1r) Now
3r2+rs2s2+2r3s
=3r2+72(1r)2+2r3(1r)
=3r2+72(1+2r+r2)+2r+3+3r
=3r2+724r2r2+2r+3+3r
=r2+r+8
=(r2+r+7)+1
=0+1
Since r is root of the equation so putting x=r in equation (1) we got r2+r+7=0.

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