Question

if alpha and beta are the zeros of p(x)=x sqaure -8x +k and alpha sqaure + beta sqaure =40 then find the value of k

Answer 1

x^2-8x+k
alpha+beta=-b/a
=8
alphaxbeta =k
alha^2+beta^2=40
now,
(alpha+beta)^2-2alphabeta=alpha^2 +beta^2
(8)^2-2 (k)=40
-2k=40-64
-2k=-24
k=24/2
k=12

Answer 2

[Let alpha denoted as a
and beta denoted as b]

p(x) = x²-8x+k

$sum \: of \: zeros \: = \frac{ - coeffiecent \: of \: x}{coefficint \: of \: {x}^{2} }$
[swipe left]

a+b= -(-8)/1

a+b = 8


$product \: of \: zeros \: = \frac{constant \: term}{coefficent \: of \: { {x}^{2} }^{2} }$

[swipe left]

ab=k/1

ab = k

given, a²+b²=40


using identity (a+b)²= a²+b²+2ab

(8)² = 40 + 2×k

64 -40 = 2k

24/2 = k

12 = k