How can we find relationship between zeros and coefficients of a polyn

1.	How can we find relationship between zeros and coefficients of a polynomial
Answer» Here the given polynomial f(x)= 2x2+ 5x\xa0-12= 2x2 + 8x - 3x -12= 2x(x + 4) - 3(x + 4)= (x + 4)(2x-3)f(x) = 0, x+4 =0 or 2x-3=0then, x = - 4 or x =\xa0{tex}\\frac{3}{2}{/tex}So, the zeros of\xa0f(x) are -4 and\xa0{tex}\\frac{3}{2}{/tex}Now,Sum of the zeros =\xa0{tex}\\left(-4+\\frac{\\displaystyle3}{\\displaystyle2}\\right)=\\frac{\\displaystyle-5}{\\displaystyle2}=\\frac{\\displaystyle-\\mathrm b}{\\displaystyle\\mathrm a}{/tex},product of the zeros =\xa0{tex}\\text{(-4)×}\\frac{\\displaystyle3}{\\displaystyle2}=\\frac{\\displaystyle-12}{\\displaystyle2}=\\frac{\\displaystyle\\mathrm c\\;}{\\displaystyle\\mathrm a}{/tex}Hence the relation of zeros and coefficients of the polynomial is verified.

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