Question

The sum of zeros = 1/3; the product of zeros = 1/2.Obtain a quadratic polynomial with the given condition.

Answer 1

sum of zeroes=1/3
product of zeroes=1/2
f(x)=x^2-(sum of zeroes)x+product of zeroes
=x^2-1/3x+1/2
=1/6(6x^2-2x+3)

Answer 2

Solution :
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If m, n are two zeroes of the

quadratic polynomial p(x),

then

p(x) = k[x² - ( m + n )x + mn],

k is a constant
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Here ,

Sum of the zeroes = m + n = 1/3 ,

Product of the roots = mn = 1/2

Required polynomial is

= k[ x² - ( m+n)x + mn ]

= k[ x² - (1/3)x + 1/2 ]

We can put different values of k.

When k = 6 ,

the quadratic polynomial will be

6x² - 2x + 3

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