Question

form a quadratic polynomial whose zeroes are 7+2√2 and 7-2√2

Answer 1

1st method and 2nd method

Answer 2

The answer is $x^2-14x+41$

Given-Quadratic polynomial whose zeroes are $7+2\sqrt{2}$ and $7-2\sqrt{2}$.

Solution-Forming the quadratic equation from given value of zeroes.

$x^2-(sum of roots)x+(product of the roots)=0$

Let the root be a and b

given roots are $7+2\sqrt{2}$ and $7-2\sqrt{2}$

Sum of roots are $=a+b$

$=7+7=14$

Product of roots are $=ab$

$=(7)^2-(2\sqrt{2})^2$

$=49-8$

$=41$

$x^2-4x+41=0$

Hence, the corresponding quadratic polynomial formed is $x^2-14x+41.$

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