4. If 2 and - 3 are the zeroes of the quadratic polynomial x2 + (a +1)x + b, then find the
values of a and b.
find a quadratic polynomial
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Step-by-step explanation:
Let, the value of x be 2
x² + ( a + 1 ) x + b = 0
⇒ 2² + ( a + 1 ) 2 + b = 0
⇒ 4 + ( a + 1 ) 2 + b = 0
⇒ 4 + 2a + 2 + b = 0
⇒ 6 + 2a + b = 0
⇒ 2a + b = - 6 _ _ _ _ _ ( 1 )
_____________________
now let the value of x be - 3
x² + ( a + 1 ) x + b = 0
⇒ (-3)² + ( a + 1 ) ( -3 )+ b = 0
⇒ 9 + -3a -3 + b = 0
⇒ 6 -3a + b = 0
⇒ -3a + b = -6
_____________________
2a + b = -3a + b
⇒ 2a + 3a = b - b
⇒ 5a = 0
⇒ a = 0
_____________________
put equation 1 here
2a + b = - 6
⇒ 2 × 0 + b = - 6
⇒ b = - 6
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