Question

If both x+2 and 2x+1 are factors of ax2 +2x+b then the value of a-b is

Answer 1

Answer:

0

Step-by-step explanation:

Method 1:

As x + 2 and 2x + 1 are factors of given polynomial. Value of polynomial must be 0 for x = - 2 & x = -1/2:

For x = - 2:

→ a(-2)² + 2(-2) + b = 0

→ b = 4 - 4a

For x = -1/2:

→ a(-1/2)² + 2(-1/2) + b = 0

→ a - 2 + 4b = 0

→ a - 2 + 4(4-4a) = 0

→ 12 = 15a → 4/5 = a

So, b = 4 - 4a = 4-4(4/5) = 4/5

So, a - b = 4/5 - 4/5 = 0

Method2:

x + 2 and 2x + 1 are factors are all two factors of the given polynomial.

So, for solutions of x + 2 and 2x + 1, those are x + 2 = 0 & 2x + 1 = 0, x = - 2 & x = -1/2:

Sum of roots = -(middle term/first term)

Here, roots are - 2 & -1/2, so

= > - 2 + (-1/2) = -(2/a)

= > (-4 - 1)/2 = - 2/a

= > -5/2 = - 2/a

= > a = 4/5

product of roots = b/a

= > (-2)*(-1/2) = b/(4/5)

= > 1 = 5b/4

= > 4/5 = b

So, a - b = 4/5 - 4/5 = 0