Question

Find a quadratic polynomial, the sum and product of whose zeros are 0

and -√2 respectively.​

Answer 1

Given:

The sum and product of whose zeros are 0  and -√2 respectively.​

To find:

The quadratic equation for the given zeroes

Solution:

If we have given the sum of the zeroes and the product of the zeroes then the quadratic equation is given by:

x²+(sum of the zeroes)x+(product of the zeroes) = 0

as per the question we have

Sum of the zeroes as 0

and

Product of the zeroes as -√2

So the quadratic equation is given as:

• x²+(sum of the zeroes)x+(product of the zeroes) = 0
• x²+0.x-√2 = 0
• x²-√2 = 0

Hence, the quadratic equation is x²-√2 = 0