Question

if alpha and bita are zeroes and the quadratic polynomial p(s)=3s^2-6s+4,then the value of alpha/bita +bita/alpha+2(1/alpha+1/bita)+3alpha bita is​

Answer 1

Answer:

alpha and beta are zeroes of 3s^2 -6s+4

So, alpha + beta = -( coefficient of s)/( coefficient of s^2)

= -(-6)/3

= 2

alpha. beta = constant/coefficient of s^2

= 4/3

Now, value of

alpha/beta + beta/alpha + 2( 1/ alpha + 1/ beta) + 3 alpha beta

(alpha^2 + beta^2)/alpha beta. + 2 ( alpha+ beta )/alpha beta + 3 alpha beta

= ( alpha^2 + beta^2 + 2 ( alpha+ beta))/alpha.beta + 3 alpha beta

=[ ( alpha + beta)^2 - 2 ( alpha beta + alpha + beta)/alpha beta ]+ 3 alpha beta

= (2)^2 - 2( 4/3 + 2)] × 3/4 + 3( 4/3)

= (4 - 8/3 - 4) × 3/4 + 4

= -8 +4

= -4

#answerwithquality #BAL

Answer 2

Answer:

alpha and beta are zeroes of 3s^2 -6s+4

So, alpha + beta = -( coefficient of s)/( coefficient of s^2)

= -(-6)/3

= 2

alpha. beta = constant/coefficient of s^2

= 4/3

Now, value of

alpha/beta + beta/alpha + 2( 1/ alpha + 1/ beta) + 3 alpha beta

(alpha^2 + beta^2)/alpha beta. + 2 ( alpha+ beta )/alpha beta + 3 alpha beta

= ( alpha^2 + beta^2 + 2 ( alpha+ beta))/alpha.beta + 3 alpha beta

=[ ( alpha + beta)^2 - 2 ( alpha beta + alpha + beta)/alpha beta ]+ 3 alpha beta

= (2)^2 - 2( 4/3 + 2)] × 3/4 + 3( 4/3)

= (4 - 8/3 - 4) × 3/4 + 4

= -8 +4

= -4