Question

if sum of squares of zeros of a quadratic polynomial p(x) = x^2 -8x + k is 40, find the value of k​

Answer 1

Answer:

Step-by-step explanation:

Let the zeros of the quadratic equation be α and β

Sum of the roots , α+β=−  

5

3

​

 

and product of the zeros , αβ=  

5

k

​

 

Also, given,

α  

2

+β  

2

=−  

25

11

​

 

Now,

(α+β)  

2

=α  

2

+β  

2

+2αβ

=>(−  

5

3

​

)  

2

=−  

25

11

​

+2×  

5

k

​

 

=>  

25

9

​

=−  

25

11

​

+  

5

2k

​

 

=>  

25

9

​

+  

25

11

​

=  

5

2k

​

 

=>  

25

20

​

=  

5

2k

​

 

=>k=  

2×25

20×5

​

 

=>k=2