Question

find the zeros of the polynomial and verify relationship between zerps and coefficient : x²-2x-8​

Answer 1

Answer:

Zeroes= -2 and 4

Step-by-step explanation:

x^2-2x-8=0

x^2-4x+2x-8=0

x(x-4)+2(x-4)=0

(x+2)(x-4)=0

Therefore, the roots are -2 and 4.

Sum of roots= -2+4=2= -b/a= -(-2)/1=2

Product of roots= -2*4= -8= c/a= (-8)/1=-8

Therefore verified.

Rate this answer 5 stars and brainliest it.

Answer 2

Step-by-step explanation:

a)   Zeros of the polynomial: $x^{2} - 2x - 8$

      $x^{2} - 2x - 8\\=x^{2} - (4 - 2)x - 8\\=x^{2} - 4x + 2x - 8\\=x(x-4) + 2(x-4)\\=(x -4) (x+2)$

    ∴  x - 4 = 0    

   or, x = 4

and  x + 2 = 0

  or,  x = -2

 ∴ Zeros are: 4, -2.

b)   Verification of relationship between zeros and coefficient:

     In the polynomial: $x^{2} - 2x - 8$,  a = 1,  b = -2,  c = -8

   ∴  α + β = 4 + (-2) = 4 - 2 = 2

and  α + β = -b/a = -(-2)/1 = 2

Again, αβ = 4(-2) = -8

and  αβ = c/a = -8/1 = -8

Hence, verified.