if zeros of polynomial x square +( A + 1 )x +b are 2 and minus 3 then find the value of (a + b)
Answers
QuesTion
If zeroes of polynomial x² + (a+1) x + b are 2 and - 3 then find the value of ( a + b).
SoluTion
given polynomial is
x² + (a + 1) x + b
given zeroes of polynomial are
2 and - 3
so,
2 + (- 3 ) = - (a + 1) / 1
- 1 = - a - 1
so,
now,
2 * - 3 = b / 1
so,
therefore,
a + b = 0 + (-6) = - 6
so,
Answer:
Step-by-step explanation:
Solution :-
P(x) = x² + (a + 1)x + b
Given, P(2) = 0 and P(- 3) = 0
Putting, P(2), we get
⇒ (2)² + (a + 1)(2) + b = 0
⇒ 4 + 2a + 2 + b = 0
⇒ 6 + 2a + b = 0
⇒ 2a + b = - 6 ... (i)
Putting, P(- 3), we get
⇒ (- 3)² + (a + 1)( - 3) + b = 0
⇒ 9 - 3a - 3 + b = 0
⇒ 6 - 3a + b = 0
⇒ - 3a + b = -6 ..... (ii)
Subtracting Eq (i) and (ii), we get
⇒ 2a + b - (- 3a + b) = - 6 - (- 6)
⇒ 2a + b + 3a - b = - 6 + 6
⇒ 5a = 0
⇒ a = 0
Putting a's value in Eq (i), we get
⇒ 2a + b = - 6
⇒ 2(0) + b = - 6
⇒ b = - 6
We have to find a + b
⇒ a + b = 0 + (- 6) = - 6
Hence, the value a + b is - 6.