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:

ax^{2} + 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)

kx^{2} – kx + k = 0

k (x^{2} – x + 1) = 0

Therefore the quadratic equation is as follows:

(x^{2} – x + 1) = 0

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