If a,b,c are rational then the root of equation (a+2b-3c )x²+(b+2c-3a

1.	If a,b,c are rational then the root of equation (a+2b-3c )x²+(b+2c-3a)x+ (c+2a-3b)=0
Answer» $\textbf{Given:}$ $(a+2b-3c)x^2+(b+2c-3a)x+(c+2a-3b)=0$ $\textbf{To find:}$ $\text{Roots of the equation}$ $\textbf{Solution:}$ $\text{Consider,}$ $(a+2b-3c)x^2+(b+2c-3a)x+(c+2a-3b)=0$ $\text{Sum of the coefficients=}(a+2b-3c)+(b+2c-3a)+(c+2a-3b)$ $=0$ $\therefore\text{(x-1) is a factor}$ $\textbf{By synthetic division}$ $\begin{array}{r\|ccc}1&a+2b-3c&b+2c-3a&c+2a-3b\\&&a+2b-3c&-c+3b-2a\\\cline{2-4}&a+2b-3c&-2a+3b-c&\|0\end{array}$ $\text{Quotient=}(a+2b-3c)x+(-2a+3b-c)$ $(a+2b-3c)x+(-2a+3b-c)=0$ $\implies\,x=\dfrac{c+2a-3b}{a+2b-3c}$ $\therefore\textbf{The roots are $1$ and $\dfrac{c+2a-3b}{a+2b-3c}$}$ Find more: If alpha,beta are the roots of equation x^2-5x+6=0 and alpha > beta then the equation with the roots (alpha+beta)and (alpha-beta) is brainly.in/question/5731128 The equation whose roots are smaller by 1 than those of 2X2 – 5x + 6 = 0 is a) 2x^2– 9x + 13 = 0 b) 2x^2– x + 3 = 0 c) 2x^2+ 9x + 13 = 0 d) 2x^2 + x + 3 = 0 brainly.in/question/16821146 Is the roots of 32 x CUBE MINUS 48 x square + 22 x minus 3 equal to zero are in AP then the MIDDLE root is brainly.in/question/17305036