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Find the zwrcesof theRyno mia.x2+t-2, and vehitre 어elanon beteen-the cofficents and十heスeroes of.thelolynoma |
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Answer» Here the given equation is x²+(1/6x)-2=0multiplying the above equation by 6 we get6x²+x-12=0or,6x²+9x-8x-12=0or,3x(2x+3)-4(2x+3)=0or,(3x-4)(2x+3)=0Hence the zeros of the polynomial arex=4/3 andx=-3/2 Now for a quadratic polynomialax²+bx+c=0the relation between coefficient a b and c and their roots m and n arem+n=-b/amn=c/a For the given equationm=4/3 n=-3/2and a=1,b=1/6 and c=-2now m+n=-1/6and -b/a=-1/6therefore,m+n=-b/aalso m x n=-2and c/a=-2Hence m x n=c/a Hence the relation between the coefficients of polynomial and its roots (or zeros) are verified. |
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