If the graph of a quadratic polynomial passes through the points (– 2, 0), (– 1, – 2), (0, – 2) and (1, 0), then find the sum of its zeroes.
Answers
Given : graph of a quadratic polynomial passes through the points (– 2, 0), (– 1, – 2), (0, – 2) and (1, 0),
To find : Sum of Zeroes
Solution:
graph of a quadratic polynomial passes through the points (– 2, 0), (– 1, – 2), (0, – 2) and (1, 0)
Zeroes are when y = 0
Hence
-2 , & 1 are Zeroes
Hence Sum of Zeroes = - 2 + 1 = - 1
Sum of Zeroes = -1
Another way :
Let say
f(x) = ax² + bx + c
(– 2, 0)
=> 0 = 4a - 2b + c
(1, 0)
=> 0 = a + b + c
=> 4a - 2b + c = a + b + c
=> 3a = 3b
=> a = b
=> b/a = 1
Sum of Zeroes = -b/a = - 1
Additional info :
Finding f(x)
(0, – 2)
=> -2 = c
0 = a + b + c
=> 0 = a + a - 2
=> a = 1
f(x) = x² + x - 2
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