Question

Find a quadratic polynomial, the sum and product of whose zeroes are
respectively 5+root 2 and 5- root 2

Answer 1

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Answer 2

The equation of quadratic polynomial

$x^2-10x+23$

Sum of zeroes=10

Product of zeroes=23

Step-by-step explanation:

$\alpha=5+\sqrt 2$

$\beta=5-\sqrt 2$

Sum of zeroes =$\alpha+\beta=5+\sqrt 2+5-\sqrt 2=10$

Product of zeroes=$\alpha \beta =(5+\sqrt 2)(5-\sqrt 2)=5^2-(\sqrt 2)^2=25-2=23$

Using identity:$(a+b)(a-b)^2=a^2-b^2$

We know that the general equation of quadratic polynomial

$x^2-(\alpha+\beta)x+\alpha\beta$

Using the formula

The equation of quadratic polynomial

$x^2-10x+23$

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