Question

If x + 2 is a factor of x square + ax -2 b and a + b is equal to 4 then​

Answer 1

if -2is factor of p(x)=x^2+ax+2b

p(-2)=(-2)^2+a(-2)+2b=0

4-2a+2b=0

2a-2b=4

2(a-b)=4

a-b=2_______(1)

a+b=4______________(2)(we know)

from 1&2

a-b=2

a+b=4

_______

2a=6

a=6/2=3

a value substitute in 1st equation

a-b=2

3-b=2

b=3-2=1

Answer 2

Given :

The  equation is

x² + a x + 2 b = 0

One of the factor of equation is x + 2

And

a + b = 4

To find :

The value of a and b

Solution :

As The quadratic equation is x² + a x + 2 b = 0

And x + 2 is its factor  ,

So,   x = -2 satisfy the equation

Put the value of x in eq x² + a x + 2 b = 0

i.e ( - 2 )² + a ( -2 ) + 2 b = 0

Or,  4  - 2 a + 2 b= 0

Or,  4 = 2 a - 2 b

i.e  a - b = 2       .......1

Since    a + b = 4          ......2

Solving eq 1 and 2

  ( a - b ) + (a + b ) = 2  +  4

Or, 2 a = 6

∴    a = $\dfrac{6}{2}$

i.e a = 3

Put the value of a into eq 1

∵  a - b = 2

So,  3 - b = 2

Or,  b = 3 - 2

i.e   b = 1

So, Value of a = 3,  and b = 1

Hence, The value of a is 3 and value of b is 1  Answer