Find a quadratic polynomial the sum and the product of whose zeroes are respectively the given numbers.
1, 1
Let the two zeroes be a and b.
The generalized form of the quadratic equation with sum and product of zeroes a and b is as follows:
ax2 + bx + c = 0 ………………… (i)
Now in this case
∴ a + b = -b/a = 1
∴ ab = c/a =1
If a = k, where k is any real integer,
b = -k ………………… (ii)
c = k ………………… (iii)
Put values from (ii) and (iii) in (i)
kx2 – kx + k = 0
k (x2 – x + 1) = 0
Therefore the quadratic equation is as follows:
(x2 – x + 1) = 0
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