Question

3+√5
30. Find a quadratic polynomial whose zeros are --
and 3.
S
(C

Answer 1

Answer:

$let \alpha \: 3 + \sqrt{5} \: and \: \beta = 3 - \sqrt{5}$

sum of zeros

$= \alpha + \beta = 3 + \sqrt{5} + 3 - \sqrt{5} = 6$

Product of zeros=

$</p><p> \alpha \beta = (3 + \sqrt{5} )(3 - \sqrt{5} ) = 9 - 5 = 4$

also sum of roots=

$\frac{ - b}{a} = \frac{ - 6}{1}$

Product of roots=

$\frac{c}{a} = \frac{4}{1}$

a=1,b= -6,c=4

HENCE,a quadratic polynomial is

${x}^{2} - 6x + 4$

Answer 2

Answer:

WE NOT THE FORMULA OF QUADRATIC EQUATION.

x^2-(alpha + beta)x +alpha*beta