Question

*(x-2) is a common factor of polynomials x² - ax + 10 & x² - bx - 2 then find the value of 'a' and 'b'.*

1️⃣ a = 7 , b = 1
2️⃣ a = -7 , b = -1
3️⃣ a = 1 , b = 7
4️⃣ a = -1 , b = -7​

Answer 1

Answer :

1️⃣ a = 7 , b = 1

Step-by-step explanation :

Given :

(x - 2) is a common factor of polynomials x² - ax + 10 & x² - bx - 2

To find :

the values of a and b

Solution :

Let

p(x) = x² - ax + 10

q(x) = x² - bx - 2

⇒ (x - 2) is a factor

x - 2 = 0

x = +2

Since it's a factor, when we put x = 2 in the polynomial ; the result is zero.

Put x = 2 in the polynomial x² - ax + 10

p(2) = 0

2² - a(2) + 10 = 0

4 - 2a + 10 = 0

14 - 2a = 0

 2a = 14

  a = 14/2

   a = 7

Put x = 2 in the polynomial x² - bx - 2

q(2) = 0

2² - b(2) - 2 = 0

4 - 2b - 2 = 0

2 - 2b = 0

 2b = 2

  b = 2/2

  b = 1

The values of a and b are 7 and 1 respectively.

Verification :

Substitute the values of a and b,

the polynomials will be x² - 7x + 10 & x² - x - 2

Now, put x = 2 and check whether the result is zero.

⟼ x² - 7x + 10

⟼ 2² - 7(2) + 10

⟼ 4 - 14 + 10

⟼  -10 + 10

⟼ 0

⟼ x² - x - 2

⟼ 2² - 2 - 2

⟼ 4 - 2 - 2

⟼ 4 - 4

⟼ 0

Since the result is zero. 2 is common zero of the given polynomials.