Question

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

Answer 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

Answer 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