Question

find a quadratic polynomial near each with the given numbers as the sum and product of its zeroes respectively ( a) 1/4 , -1 (b) -1/4 , 1/4 (c) 4,1​

Answer 1

Answer:

Given: Sum of zeroes =α+β=1/4  

Product of zeroes =αβ=−1  

Then, the quadratic polynomial =x  

2

−( sum of zeroes )x+ product of zeroes =x  

2

−(  

4

1

​

)x+(−1)

=x  

2

−  

4

x

​

−1

=  

4

4x  

2

−x−4

​

 

We can consider 4x  

2

−x−4 as required quadratic polynomial because it will also satisfy the given conditions.