Question

find the zeros of the following quadratic polynomial and verify the relationship between zeros and the coefficients x²-5x​

Answer 1

Step-by-step explanation:

x²-5x =0

=>x(x-5)=0

=>x=0 and x=5

Hence the zeroes are 0 and 5.

Therefore, a=1 , b= -5 , c=0

Verification:-

•Sum of the zeroes= -b/a

=-(-5)/1

= 5

•Product of zeroes = c/a

= 0/1

=0

Hence proved.

And that's all your answer

Answer 2

Answer:

zeroes are 2 and 3

Step-by-step explanation:

let the zeroes of the polynomial= alpha and beta.

p(x)=x²-5x=   x²-5x+6

                   ax²+bx+c

                a=1,b=-5,c=6

         by splitting middle term

 = x²-2x-3x+6

 = x(x-2) -3(x-2)

 = (x-2)(x-3)

x-2=0

x=2= alpha

x-3=0

x=3=beta.

verification

sum of zeroes= alpha+beta =2+3= 5

sum of zeroes= alpha+beta= -b/a = -(-5)/1= 5

product of zeroes = alpha x beta = 2*3=6

product of zeroes = alpha x beta = c/a = 6/1 = 6

hence verified.