Question

Find the zeroes of a quadratic polynomial 2x2 + 3x - 14 and verify the relationship between the zeroes and its coefficients.​

Answer 1

Answer:

2x^2 +3x - 14

2x^2 + (7 - 4)x - 14

2x^2 + 7x - 4x - 14

x(2x + 7) - 2(2x + 7)

(2x + 7) (x - 2)

x = 7/2 , x = 2.

Answer 2

Answer:

plz look at the ans below

Step-by-step explanation:  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.