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Question

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.

2,13

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Solution

Sum of zeros =2

Product of zeros =13

Let the polynomial be ax2+bx+c, and its zeroes be α and β.

α+β=2.

αβ=13

Quadratic polynomial =x2(Sum of zeroes)x+(Product of zeros)

=x22x+13

=13[3x232x+1]

Quadratic polynomial is 3x232x+1.


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