Question

Find the zeroes of the following quadratic polynomial and verify the relationship between zeroes and the coefficients 2x²-x-6.​

Answer 1

Answer:

2x

2

−x−1=0

⇒ 2x

2

−2x+x−1=0

⇒ 2x(x−1)+1(x−1)=0

⇒ (x−1)(2x+1)=0

⇒ x=1 and x=

2

−1

∴ Required zeros are α=1 and β=−

2

1

Now, we are going to verify relationship between the zeros and the coefficient.

2x

2

−x−1=0

⇒ Her, a=2,b=1,c=−1

⇒ α+β=

a

−b

⇒ 1+(

2

−1

)=−

2

−1

⇒

2

1

=

2

1

∴ L.H.S.=R.H.S.

⇒ αβ=

a

c

⇒ 1(

2

−1

)=

2

−1

⇒

2

−1

=

2

−1

∴ L.H.S.=R.H.S.