find the zero of the quadratic polynomial and verify the relationship between zero and Coefficient first x square – 2 x minus​

2 thoughts on “find the zero of the quadratic polynomial and verify the relationship between zero and Coefficient first x square – 2 x minus​”

1. Answer:

   f(x)=x

   2

   −2x−8

   ⇒f(x)=x

   2

   −4x+2x−8

   ⇒f(x)=x(x−4)+2(x−4)]

   ⇒f(x)=(x−4)(x+2)

   Zeros of f(x) are given by f(x) = 0

   ⇒x

   2

   −2x−8=0

   ⇒(x−4)(x+2)=0

   ⇒x=4 or x=−2

   So, α=4 and β=−2

   ∴ sum of zeros =α+β=4−2=2

   Also, sum of zeros =

   Coefficient of x

   2

   Coefficient of x

   =

   1

   −(−2)

   =2

   So, sum of zeros =α+β=−

   Coefficient ofx

   2

   Coefficient of x

   Now, product of zeros =αβ=(4)(−2)=−8

   Also, product of zeros =

   Coefficient ofx

   2

   Constant term

   =

   1

   −8

   =−8

   ∴ Product of zeros =

   Coefficient of x

   2

   Constant term

   =αβ

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2. Answer:

   The quadratic polynomial is:x square-2x

   first,take x as common then we get x(x-2)

   first x=0 and second x=2

   so two zeros of the given quadratic polynomial

   are 0 and 2. ans.

   we represent zeros of the quadratic polynomial by alpha and beta so to verify it

   use the following formula,

   alpha+ beta=-b/a

   and,alpha×beta=c/a.

   Hope it will help you

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