Question

2. Find a quadratic polynomial each with the
given numbers as the sum and product of
its zeroes respectively. From that, find the
zeroes of the polynomial :
21
* (1)
1
5
16
* (2)26. -
2​

Answer 1

Step-by-step explanation:

If α and β are the zeroes of a quadratic polynmial, then the polynomial can be written as follows-

p(x)=x2−(α+β)x+(αβ)

Whereas

α+β= Sum of roots

αβ= Product of roots

Now according to the question,

Sum of roots =α+β=0

Product of roots =αβ=5

Therefore the quadratic polynomial will be-

p(x)=x2−(0)x+(5)

⇒p(x)=x2+5

Hence the quadratic polynomial will be x2+5.