Question

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Answer 1

Explanation

if 'n' is zero of the polynomial P (x)

then, P (n) = 0

that is put 'n' in place of 'x' in polynomial.

Question

P (x) = 3x^2 - 3 x + 7a

given,

2 is a zero of the polynomial.

put '2' in place of 'x' in polynomial

P (x) = 3x^2 -3x + 7a

P (2) = 3 (2)^2 -3 (2) + 7a

0 = 3 (4)-6 + 7a

0 = 12-6 + 7a

0 = 6 + 7a

-6 = 7a

a = -6/7

Note :-

^2= symbol of square

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Answer 2

Given :–

• A polynomial, p(x) = 3x² – 3x + 7a.
• 2 is a zero of the polynomial.

To Find :–

• Value of a.

Solution :–

Given polynomial,

• 3x² – 3x + 7a

Zero of the given polynomial is x = 2.

Now, put 2 in the place of x.

We get,

⟹ 3(2)² – 3(2) + 7a = 0

⟹ 3 × 4 – 6 + 7a = 0

⟹ 12 – 6 + 7a = 0

⟹ 6 + 7a = 0

Now, add –2 both sides, we get,

⟹ 6 + 7a – 2 = 0 – 2

⟹ 6 – 2 + 7a = –2

⟹ 4 + 7a = –2

⟹ 7a = –2 – 4

⟹ 7a = –6

⟹ a = $\dfrac{-6}{7}$

Hence,

The value of a is $\dfrac{-6}{7}$

Check :–

Values,

• x = 2
• a = $\dfrac{-6}{7}$

Now, put both the values in the given polynomial.

Given polynomial,

⟹ 3x² – 3x + 7a

So,

⟹ 3(2)² – 3(2) + 7$(\dfrac{-6}{7} )$

⟹ 3 × 4 – 6 + $\cancel7 (\dfrac{-6}{\cancel{7}})$

After open the bracket.

We get,

⟹ 12 – 6 – 6

⟹ 6 – 6

⟹ 0

Since, we get zero (0).

So, the value of a = $\dfrac{-6}{7}$ is correct.