Question

plzz help ..........if alpha and beta are the zeroes of polynomial ax^2+bx+c then prove that alpha+beta=-b/a,alpha/beta =c/a​

Answer 1

Answer:

hey here ur answer......consider @ as alpha and & as beta for the time being.....there is no typing option

Step-by-step explanation:

Let @and & be the zeroes of the quadratic polynomial

p(x)=ax^2+bc+C

then, (x-@) and (x-&) are the factors of p(x)

therefore, (ax^2+bc+C)=k(x-@)(x-&),where k is constant.

=k.{x^2-(@+&)x+@&}

=kx^2-k(@+&)x+k(@&).

on comparing coefficients of like powers of x on the both sides ,we get

k=a,-k(@+&)=b and k(@&)=C

= -a(@+&)=b and a(@&)=C

=(@+&)=-b/a and @&=c/a

therefore ,

sum of zeroes = -(coefficient of x)

(coefficient of x^2)

product of zeroes=(constant term)

(coefficient of x^2)

hope u understood

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