Question

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. Class 10

Answer 1

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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