Question

find a quadratic polynomial whose zeros are 5 + root 2 and 5 minus root 2

Answer 1

$\huge\mathsf{Given \ -}$
$<b>$
Let the two zeroes be $\alpha$ and $\beta$.

•°•

$\alpha = 5 + \sqrt{2}$

And

$\beta = 5 - \sqrt{2}$

Sum of zeroes (S) -

$= \alpha + \beta$

= (5 + √2) + (5 - √2)

= 10

Product of zeroes (P) -

$= \alpha \beta$

= (5 + √2)(5 - √2)

Using identity -

(a + b)(a - b) = a² - b²

= (5)² - (√2)²

= 25 - 2

= 23

The required polynomial is :-

f(x) = x² - (S)x + (P)

f(x) = x² - (10)x + (23)
$<marquee>$
$\huge\mathsf\red{\boxed{f(x) \ = \ x^2 - 10x + 23}}$

Answer 2

Answer:

Step-by-step explanation:

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