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  • For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation 21 /8

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation 21 /8

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Answer.         \left [\frac{5}{2}, \frac{1}{8} \right ]

Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.

Here, sum of zeroes =\frac{21}{8}

Product of zeroes =\frac{5}{16}

Let p(x) is the required polynomial

p(x) = x2 – (sum of zeroes)x + (product of zeroes)

=x^{2}+\left (\frac{-21}{8} \right )x+\frac{5}{16}

=x^{2}-\frac{-21}{8} x+\frac{5}{16}

Multiply by 16 we get

p(x) = 16x^2 - 42x + 5

Hence, 16x^2 - 42x + 5 is the required polynomial

p(x) = 16x^2 - 42x + 5

= 16x^2 - 40x -2x + 5

8x(2x - 5) - 1(2x - 5)

(2x - 5) (8x - 1)

x=\frac{5}{2}, \frac{1}{8}  are the zeroes of p(x).

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