Question

if alpha and beta are zeros of polynomial f(x)=x2-6x+k find value of k such that alpha2 +beta2 =40

Answer 1

Answer:

Step-by-step explanation:

f(x)=x2-6x+k;

by comparing this eq. with ax2+bx+c = 0;

we get a = 1, b = -6  and c = k;

Suppose the roots of the equation is alpha and beta:

alpha + beta = -b/a

alpha+beta = 6/1;

alpha*beta = c/a;

alpha*beta = k

we know that:

(a+b)2 = a2+b2+2ab ;

Not putting the values in above eq.;

(6)2 = 40 + 2k;

36 - 40 = 2k;

-4 = 2k;

k= -2

Answer 2

Answer:

K = -2

Step-by-step explanation:

f(x) = x² - 6x + k (Given)

By comparing ax² + bc + c

a = 1 , b = -6 , c = k

Now,

alpha + beta = -b/a = -(-6)/1 = 6

alpha × beta = c/a = k/1 = k

We know that,

(x+y)² = x² + y² + 2xy

(x+y)² - 2xy = x² + y²

Then,

(alpha + beta)² = alpha² + beta² + 2alpha×beta

(alpha + beta)² - 2alpha×beta = alpha² + beta² (equation 1)

alpha² + beta² = 40 (Given)

(alpha+beta)² - 2alpha×beta = 40 (from equation 1)

(6)² - 2k = 40

36 - 2k = 40

-2k = 40 - 36

-2k = 4

k = 4/-2

k = -4/2

k = -2