Question

Find the quadratic polynomial whose zeros are 5 minus 3 root 2 and 5 + 3 root 2

Answer 1

In a quadric polynomial,

$\small{\bold{p(x) = k(x^2 - (\alpha + \beta)x + \alpha \beta)}}$

Here the two zeros given are $\bold{5 - 3\sqrt{2}\:and\:5 - 3\sqrt{2}}$

Sum of zeros :

$\Longrightarrow{\bold{ 5 - 3\sqrt{2} + 5 + 3\sqrt{2}}}$

⇒10

Product of zeros :

$\Longrightarrow{\bold{ (5 - 3\sqrt{2})(5 + 3\sqrt{2})}}$

⇒ 25 - 18

⇒ 7

So the polynomial formed is

= k(x² - 10x + 7) where k stands for any real and constant number.

$\large{\boxed{\bold{k(x^2 - 10x + 7)}}}$

Answer 2

given,

5-3√2 and 5+3√2 are roots of equation

quadratic equation = x² -(α+β)x+αβ

=>x²-(5-3√2+5+3√2)x+(5-3√2)(5+3√2)

=>x²-10x+(25-18)

=>x²-10+7