Question

find the quadratic polynomial from the sum of zeroes of the quadratic polynomial is 0 and the product of zeroes is√5​

Answer 1

Answer:

x^2+root5

Step-by-step explanation:

-b/a=0

b=0, a=1

c/a=root5

c=root 5

a=1

Answer 2

Given :-

• Sum of zeroes of Quadratic polynomial is 0
• Product of zeroes of Quadratic polynomial is√5

To find :-

Quadratic polynomial

Solution:-

If ${\alpha,\beta}$ are roots of Quadratic polynomial

then required polynomial is

$x {}^{2} - ( \alpha + \beta )x + \alpha \beta$

$sum \: of \: roots \: = \alpha + \beta$

$\alpha + \beta = 0$

$product \: of \: roots \: = \alpha \beta$

$\alpha \beta = \sqrt{5}$

Substituting values in formula

$x {}^{2} - ( \alpha + \beta )x + \alpha \beta$

$x {}^{2} - (0)x + \sqrt{5}$

$x {}^{2} - 0 + \sqrt{5}$

$x {}^{2} - \sqrt{5}$

So, Required Quadratic polynomial is$x {}^{2} - \sqrt{5}$