Question

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

please solve it my H.W

1) 1/4, -1

2) 0,√5

3) 4,1

4) 1,1
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Answer 1

Given :-

★ The sum and the product of zeros are

1. ¼ , -1

2. 0, √5

3. 4,1

4. 1,1 respectively.

To Find :-

★ A quadratic polynomial

Solution :-

We know,

Required polynomial is given by

x² - ( α + β) x + αβ =0............... eq(1)

1. Let the zeroes of polynomial be α and β.

According to the question

α + β = ¼

αβ =-1

Now, put the given values eq(1)

x² - ( α + β) x + αβ =0

= x² - ¼ x -1

=4x² -x -4

Hence, required polynomial is = 4x² -x -4

2. Let the zeroes of polynomial be α and β.

According to the question

α + β = 0

αβ = √5

Now, put the given values eq(1)

x² - ( α + β) x + αβ =0

= x² - 0 × x +√5

= x² +√5

Hence, required polynomial is = x² +√5

3.Let the zeroes of polynomial be α and β.

According to the question

α + β = 4

αβ =1

Now, put the given values eq(1)

x² - ( α + β) x + αβ =0

= x² - 4x +1

Hence, required polynomial is = x² - 4x +1

4.Let the zeroes of polynomial be α and β.

According to the question

α + β = 1

αβ =1

Now, put the given values eq(1)

x² - ( α + β) x + αβ =0

= x² -1x +1

= x² - x +1

Hence, required polynomial is = x² - x +1

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