Q4 of 64 Page 43

Obtain a quadratic polynomial with the following conditions:

The sum of zeros = 2; the product of zeros = —3

Let α and β be the zeros of the polynomial p(x) = ax2 + bx + c.


Given, α + β = 2 ; αβ = –3


We know that α + β = – = – . So, – = = k, say


Thus, b = –2k, a = k


And αβ = = – . So, c = –3a = –3(k) = –3k


p(x) = ax2 + bx + c


∴ p(x) = (k)x2 + (–2k)x – 3k


∴ p(x) = k (x2 – 2x – 3)


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