Question

Find a quadratic polynomial whose zeros are 4 + root 2 divided by 2 and 4 minus root device

Answer 1

Answer:

The required quadratic polynomial is $x^2-4x+\frac{7}{2}$

Step-by-step explanation:

Given zeros are

$\frac{4+\sqrt2}{2}\:and\:\frac{4-\sqrt2}{2}$

sum of the zeros

$=\frac{4+\sqrt2}{2}+\frac{4-\sqrt2}{2}\\\\=\frac{4+\sqrt2+4-\sqrt2}{2}\\\\=\frac{8}{2}\\\\=4$

product of the zeros

$=(\frac{4+\sqrt2}{2})(\frac{4-\sqrt2}{2})\\\\=\frac{4^2-(\sqrt2)^2}{4}\\\\=\frac{16-2}{4}\\\\=\frac{14}{4}\\\\=\frac{7}{2}$

The required quadratic polynomial is

$x^2-(sum\:of\:the\:zeros)x+(product\:of\:the\:zeros)\\\\x^2-4x+\frac{7}{2}$

Answer 2

Answer:

2x² - 8x + 7

Step-by-step explanation:

Find a quadratic polynomial whose zeros are 4 + root 2 divided by 2 and 4 minus root 2 divided by 2

roots are

(4 + √2)/2  & (4 - √2) /2

= 2 + 1/√2     & 2 - 1/√2

F(x) = ( x - (2 + 1/√2))(x - (2 - 1/√2))

= x² - x(2 + 1/√2 + 2 - 1/√2) + ( (2 + 1/√2) (2 - 1/√2)

= x² -4x + (4 - 1/2)

= x² - 4x + 7/2

= 2x² - 8x + 7