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

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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