Question

P and Q are the zeros of the polynomial 4y^2 - 4y + 1.
Then what should be the value of 1/p + 1/q + pq = ?

Answer 1

Question:

If p and q are the zeros of the polynomial 4y^2 - 4y + 1 , then what should be the value of ;

1/p + 1/q + pq ?

Solution:

Here,

The given quadratic polynomial is

4y^2 - 4y + 1.

Now, we know that,

Sum of zeros = -b/a

Thus;

=> p + q = -(-4)/4

=> p + q = 1 -------(1)

Also;

Product of zeros = c/a

Thus;

=> p•q = 1/4 ---------(2)

Now,

1/p + 1/q + pq = {p+q+(pq)^2}/pq

= {1 + (1/4)^2 }/(1/4)

= { 1+ 1/16 }/(1/4)

= {(16+1)/16}/(1/4)

= (17/16)/(1/4)

= 4•(17/16)

= 17/4

Hence, the required value of

1/p + 1/q + pq is 17/4.

Other method;

The given quadratic polynomial is

4y^2 - 4y + 1 and p & q are its zeros.

In order to find the zeros of the polynomial, equate it to zero.

Thus;

=> 4y^2 - 4y + 1 = 0

=> (2y)^2 - 2•2y•1 + (1)^2 = 0

=> (2y - 1)^2 = 0

=> y = 1/2 , 1/2

Here, p = 1/2 and q = 1/2.

Thus;

1/p + 1/q + pq

= 1/(1/2) + 1/(1/2) + (1/2)•(1/2)

= 2 + 2 + 1/4

= (8 + 8 + 1)/4

= 17/4

Hence, the required value of

1/p + 1/q + pq is 17/4.

Answer 2

Answer:17/4

Step-by-step explanation:4y^2 -4y +1

4y^2-(2y+2y)+1 =4y^2-2y -2y+1

=2y(2y-1)-1(2y-1)=(2y-1)(2y-1) so p=1/2 and q=1/2 .put values answer will come.