Question

If α and β are the zeros of the polynomial x2−8x+k such that α2+β2 =50, then the value of k is​

Answer 1

Answer:

k=7

Step-by-step explanation:

x2-8x+k

Sun of zeros=a+b=-b/a=8

Product of zeros=ab=c/a=k

a2+b2=50(given)

(a+b)2-2ab=50

(8×8)-2×k=50

64-2k=50

2k=14

k=7

Answer 2

Answer:

k= 12

Step-by-step explanation:

p(x)=x  ^2 −8x+k

a=1,

b=−8,

c=k

α+β=  a −b  =8,

αβ=  a

c =k,  

α  ^2  +β  ^2  =40

α  ^2  +β  ^2  =(α+β) ^2  −2αβ

40=8 ^2  −2k

2k=24

k=12