Look what I shared! @MIUI
Answers
Question:
If the zeroes of the quadratic polynomial x² + ( a + 1 ) x - b are 2 and - 3, then
A) a = - 7, b = - 1
B) a = 5, b = - 1
C) a = 2, b = - 6
D) a = 0, b = - 6
Answer:
The values of a and b are 0 and - 6 respectively.
Option D) a = 0, b = - 6
Step-by-step-explanation:
The given quadratic polynomial is x² + ( a + 1 ) x + b.
The zeroes of the polynomial are 2 and - 3.
As 2 is a zero of the polynomial, by substituting x = 2 it satisfies the equation
x² + ( a + 1 ) x + b = 0
⇒ ( 2 )² + ( a + 1 ) * 2 + b = 0
⇒ 4 + 2a + 2 + b = 0
⇒ 4 + 2 + 2a + b = 0
⇒ 2a + b + 6 = 0
⇒ 2a + b = - 6
⇒ b = - 6 - 2a
⇒ b = - 2a - 6 - - - ( 1 )
Also, as - 3 is a zero of the polynomial, by substituting x = - 3 it satisfies the equation
x² + ( a + 1 ) x + b = 0
⇒ ( - 3 )² + ( a + 1 ) * - 3 + b = 0
⇒ 9 - 3a - 3 + b = 0
⇒ - 3a + b + 9 - 3 = 0
⇒ - 3a + b + 6 = 0
⇒ - 3a + ( - 2a - 6 ) + 6 = 0 - - - [ From ( 1 ) ]
⇒ - 3a - 2a - 6 + 6 = 0
⇒ - 5a = 0
⇒ a = 0 / - 5
⇒ a = 0
By substituting a = 0 in equation ( 1 ),
b = - 2a - 6 - - - ( 1 )
⇒ b = - 2 * 0 - 6
⇒ b = 0 - 6
⇒ b = - 6
∴ The values of a and b are 0 and - 6 respectively.
Answer:
8a ndn nsjdakvdlbsje kdbwbssbbw snsvsbjs snsvs a snaw she qjejs d n se bakwas sjbs d en snwwbs d ebebvsskd 9406