Question

find a quadratic polynomial sum and product of whose zeros are 2 and root 5 respectively​

Answer 1

Sum of the roots = -b/a = 2 + root5 (alpha + beta)

Product of the roots = c/a = 2 x root 5 (alpha x beta)

a = 1 , b = - 2 - root 5 , c = 2 x root 5

Now we can form the polynomial based on the above values.

x^2 + (-2-root5)x+ 2xroot5 is the required polynomial.

edit : I'm sorry. I misread the question as 5.

Answer 2

$\huge\orange{\boxed{\purple{\mathbb{\overbrace{\underbrace{\fcolorbox{orange}{cyan}{\underline{\red{ANSWER}}}}}}}}}$

$a + b = 2$

$ab = \sqrt{5}$

${x}^{2} + (a + b)x + ab = 0$

$By \: putting \: the \: value \: we \: get,$

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

$☆ \: Hence \: Verified \: ☆$