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Question:

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

**(i) 1/4 ** **, 1 (ii) ** **, 1/3**** (iii) 0, **

**(iv) 1, 1 (v) -1/4****, **** 1/4 (vi) 4,1**

Answer:

**Solutions: **

**(i) 1/4 ** **, 1 **

**Given, the sum of zeroes ** ** ****is 1/4 ** ** and the product of zeroes ** **is 1.**

**We know that the quadratic equation formula is ** ** – (sum of the root)** ** + (product of root) = 0.**

**Substitute the given values in the formula, we get**

**Hence, the quadratic polynomial is ** ** **.

**(ii) ** **, 1/3**** **

**Given, the sum of zeroes **** ****is ** ** and the product of zeroes ** **is 1/3.**

**We know that the quadratic equation formula is ** ** – (sum of the root)** ** + (product of root) = 0.**

**Substitute the given values in the formula, we get**

**Hence, the quadratic polynomial is **.

**(iii) 0, **

**Given, the sum of zeroes **** ****is 0 ** ** and the product of zeroes ** **is .**

**We know that the quadratic equation formula is ** ** – (sum of the root)** ** + (product of root) = 0.**

**Substitute the given values in the formula, we get**

**Hence, the quadratic polynomial is **.

**(iv) 1, 1 **

**Given, the sum of zeroes **** ****is 1 ** ** and the product of zeroes ** **is 1.**

**We know that the quadratic equation formula is ** ** – (sum of the root)** ** + (product of root) = 0.**

**Substitute the given values in the formula, we get**

**Hence, the quadratic polynomial is ** .

**(v) -1/4****, **** 1/4**

**Given, the sum of zeroes **** ****is -1/4 ** ** and the product of zeroes ** **is 1/4.**

**We know that the quadratic equation formula is ** ** – (sum of the root)** ** + (product of root) = 0.**

**Substitute the given values in the formula, we get**

**Hence, the quadratic polynomial is ** .

**(vi) 4,1 **

**Given, the sum of zeroes **** ****is 4 ** ** and the product of zeroes ** **is 1.**

**We know that the quadratic equation formula is ** ** – (sum of the root)** ** + (product of root) = 0.**

**Substitute the given values in the formula, we get**

**Hence, the quadratic polynomial is ** .

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