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Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively (i) $\frac{1}{4}, -1$ (ii) $\sqrt{2}, \frac{1}{4}$ (iii) $0, \sqrt{5}$ (iv) $1, 1$ (v) $- \frac{1}{4}, \frac{1}{4}$ (iv) $4, 1$

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

(i) $\frac{1}{4}, -1$

(ii) $\sqrt{2}, \frac{1}{4}$

(iii) $0, \sqrt{5}$

(iv) $1, 1$

(v) $- \frac{1}{4}, \frac{1}{4}$

(iv) $4, 1$

 

This Question has 1 answers.

The quadratic polynomial with given sum and product of zeroes can be found using the standard form:

x2(sum of zeroes)x+(product of zeroes)=0

(i) Given sum = 14, product = 1

x214x1=0

(ii) Given sum = 2, product = 14

x22x+14=0

(iii) Given sum = 0, product = 5

x2+5=0

(iv) Given sum = 1, product = 1

x2x+1=0

(v) Given sum = 14, product = 14

x2+14x+14=0

(vi) Given sum = 4, product = 1

x24x+1=0

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