Question

Topic:- Quadratic Equations

Answer 1

If Alpha and Beta are the roots of the equation
\[\Large x^2-2x+3=0\]
Find the equation whose roots are
\[\Large \alpha^3-3\alpha^2+5\alpha -2 \]
\[\Large \beta^3-\beta^2+\beta+5\]

Answer 2

alpha=>a
a^3-3a^2+5a-2
=a(a^2-2a+3) - a^2+2a-2
=a(a^2-2a+3)-(a^2-2a+3)+1
=0-0+1
=1

Answer 3

Beta=>b
b^3-b^2+b+5
=b(b^2-2b+3) +b^2-2b+5
=b(b^2-2b+3) + (b^2-2b+3) +2
=0+0+2
=2

Answer 4

got!

Answer 5

Hence the required equation would be (x-1)(x-2)=x^2-(1+2)x+2=x^2-3x+2

Answer 6

Thanks a lot

Answer 7

well, it was fun...

Answer 8

yeah , i was on this problem for 15 min