Question

find the zero of the quadratic polynomial X^2 +X and verify the relationship between the zero and the cofficient​

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.

Step-by-step explanation:

Answer 2

Answer:

The relationship between zeros and coefficients is verified.

Step-by-step explanation:

Find the zeros,

$\longrightarrow$ x² + x

$\longrightarrow$ x(x + 1)

$\longrightarrow$ (x)(x + 1)

Zeros,

$\longrightarrow$ x + 1 = 0

$\longrightarrow$ x = -1

$\longrightarrow$ x = 0

Zeros are -1 and 0.

So, let α and β be (-1) and 0.

___________________

Verifying the relationship between zeros and coefficients.

In the polynomial,

• a = 1
• b = 1
• c = 0

________________________

★ Sum of zeros:

$\longrightarrow$ 0 + (-1)

$\longrightarrow$ -1 ---- (I)

$\longrightarrow$ α + β = -b/a

$\longrightarrow$ α + β = -(1)/1

$\longrightarrow$ α + β = -1 ---- (II)

________________________

★ Product of zeros:

.$\longrightarrow$ 0 × (-1)

$\longrightarrow$ 0 ---- (III)

$\longrightarrow$ αβ = c/a

$\longrightarrow$ αβ = 0/1

$\longrightarrow$ αβ = 0 ---- (IV)

I and II are equal. III and IV are equal.

Hence, the relationship between zeros and coefficients is verified.