Question

find the quadratic polynomial whose sum and product of zeros are 0 and root 5 respectively​

Answer 1

Given:

Sum of zeroes of a polynomial= 0

Product of zeroes of a polynomial=√5

To find:

A quadratic polynomial

Solution:

We can find the solution by following the steps given below-

We know that the general form of a quadratic polynomial is

${x}^{2} - (sum of zeroes)x + (product of zeroes)$

On putting the values, we get

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

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

Therefore, the quadratic polynomial is

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

Answer 2

Answer:

Given that the sum and product of zeros of quadratic polynomial are 0 and √5 , respectively. Therefore, −ba=0 − b a = 0 and ca=√5. c a = 5 . ... Therefore, the quadratic polynomial is p(x) = ax2 + √5 a, where a is any real number.