Q. 2 F5.0( 3 Votes )

Find a quadratic polynomial the sum and the product of whose zeroes are respectively the given numbers.

1, 1

Answer :

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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