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Find a quadratic polynomial each with th...

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.(i) `1/4,-1` (ii) `sqrt(2),1/3` (iii) `0,sqrt(5)`(iv) `1,1`(v) `-1/4 , 1/4 `(vi) `4, 1`

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To find a quadratic polynomial given the sum and product of its zeroes, we can use the standard form of a quadratic polynomial, which is: \[ P(x) = x^2 - (sum \ of \ roots) \cdot x + (product \ of \ roots) \] Let's solve each part step by step. ### (i) Given: Sum = \( \frac{1}{4} \), Product = -1 ...
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