Question

find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficient of x square - 2 x equals to 2​

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 = $\alpha +\beta =4-2=2$

also coefficient of x  /coefficient of x ^2

=  -[-2]/1  =   2

So, sum of zeros =α+β   =   - coefficient of x  /coefficient x^2

Now, product of zeros =αβ=(4)(−2)=−8

Also, product of zeros =  Constant term /coefficient of x^2

=  −8/1       = −8

∴ Product of zeros =Constant term /coefficient of x^2=$\alpha \beta$

hope it helps

tq........//////

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Step-by-step explanation: