Question

Find the zeroes of the quadratic polynomial i) x2 – 3 ii) x2–2x–8 and verify the relationship between
zeroes and coefficients.
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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