Question

if -2 is a zero of the polynomial px =x2+ax +2b and a+b=4 than

Answer 1

Answer:

Step-by-step explanation:

let p (×) = x² + ax + 2b

if x + 2 is a factor of p (x)

then by factor Theroem

p ( - 2 ) = 0

( - 2 )² + a ( - 2 ) + 2b = 0

4 - 2a + 2b = 0

a - b = 2  ( ii )

also given that a + b = 4( ii )

Adiing (i) and (ii) we get

2a = 6

a = 3

putting a = 3 in (i) we get

a - b = 2

3 - b = 2

b = 1

therefore we get a = 3 and b = 1

Answer 2

p(x) = x² + 3x + 2 if  -2 is a zero of the polynomial p(x) =x²+ax +2b and a+b=4 , also a = 3 , b = 2

Given:

• Polynomial p(x) = x² + ax + 2b
• -2 is a zero
• a + b = 4

To Find:

• Value of a and b
• Polynomial

Solution:

"If m is a zero of the polynomial p(x) then p(m) = 0"

Step 1:

Substitute x=-2  in p(x) and simplify:

(-2)² + a(-2) + 2b = 0

=> 4 - 2a + 2b = 0

=> 2a - 2b = 4

=> a - b = 2

Step 2:

Add a - b = 2  and a + b = 4 and solve for a:

a - b + a + b = 2 + 4

=> 2a = 6

=>  a= 3

Step 3:

Substitute a=3  in a + b = 4 and solve for b:

3 + b = 4

=> b = 1

Step 4:

Substitute a=3  and b = 1 in p(x)=x² + ax + 2b

p(x) = x² + 3x + 2

p(x) = x² + 3x + 2 if  -2 is a zero of the polynomial p(x) =x²+ax +2b and a+b=4 , also a = 3 , b = 2

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