Question

Find a quadratic polynomial whose sum and product of its zeroes are 1 and 1 respectively.
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

The quadratic polynomial sum and product of its zeroes are 1 and 1 is $x^{2} -x+1=0.$

Given,

In any quadratic polynomial, the sum of zeroes is 1.

And the product of zeroes is 1.

To Find,

The quadratic polynomial with given conditions.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

The process to deduce a quadratic polynomial with given sum and product of zeroes is as follows:

Suppose the roots of a quadratic equation are α and β.

The sum of roots/zeroes (α+β) and the product αβ.

Then the quadratic equation will be, $x^{2} -(\alpha+ \beta)x+\alpha \beta =0.$

So here already given that sum of zeroes is 1 and product is 1.

So, the equation will be $x^{2} -1.x+1=0.$

Hence, The quadratic polynomial sum and product of its zeroes are 1 and 1 is $x^{2} -x+1=0.$

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