Question

If (x-6) is the factor of P(x) = x^{2} - (4a-1)x + 2b and Q(x) = x^{2} - (2a-5)x + 6b then what is b-a?
Help please.

Answer 1

Answer:

-10

Step-by-step explanation:

(i)

Given, P(x) = x² - (4a - 1)x + 2b

Since, (x - 6) is the factor of p(x), then p(6) = 0

P(6) = (6)² - (4a - 1)6 + 2b

⇒ 0 =  36 - 24a + 6 + 2b

⇒ 0 = 42 - 24a + 2b

⇒ -24a + 2b = -42

(ii)

Given, Q(x) = x² - (2a - 5)x + 6b

Since, (x - 6) is a factor of f(x), So f(6) = 0

f(6) = (6)² - (2a - 5)6 + 6b

⇒ 0 = 36 - 12a + 30 + 6b

⇒ 0 = 66 - 12a + 6b

⇒ -12a + 6b = -66

On solving (i) & (ii) * 2, we get

⇒ -24a + 2b = -42

⇒ -24a + 12b = -132

   --------------------------

               -10b = 90

                 b = -9

           

Substitute b = -9 in (i), we get

⇒ -24a + 2b = -42

⇒ -24a + 2(-9) = -42

⇒ a = 1

Now,

b - a = -9 - 1

        = -10

Hope it helps!

Answer 2

Since (x-6) is a factor of the equations,

Value of x=6

Put the value of x in both the equations

Then you will get 1--------24

a-2b=42

2-----12a-6b=66

Solve the equations

Get the value of a and b