Question

8. If ax+ bx + c and br? + ax + c have a common factor x + 1 then show that
c=0 and a = b.

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Answer 1

Step-by-step explanation:

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Answer 2

Appropriate Question:

★ If ax² + bx + c and bx² + ax + c have a common factor x+1 then show that c = 0 and a = b.

Given:

• ax² + bx + c and bx² + ax + c

• Common factor : x + 1

To Find:

• c = 0, a = b

Solution:

Let x + 1,

→ x - 1 = 0

→ x = 1

Here,

• p(x) = ax² + bx + c
• f(x) = bx² + ax + c

As we know,

• They have common factor and it's remainder zero when divided by x - 1.

According to a question:

• p(x) = 0
• f(x) = 0

¶utting x = 1

★ p(x) = a(1)² + b(x) + c = 0

→ a -b + c = 0 ---(1)

★ f(x) = b(1)² + a(1) + c = 0

→ b - a+ c = 0 ---(2)

Adding (1) + (2)

→ a - b + c = 0 + b - a + c = 0

a and b get cancelled.

→ 2c = 0

→ c = 0

Substitute c = 0 in 1st equation,

→ a - b + 0 = 0

→ a = b

Hence,

• c = 0
• a = b