Question

if p and q are the zeroes of the polynomial f(x)=x2-5x+k such that p-q=1,find the value of k

Answer 1

Heya !!!






P(X) = X²-5X+K





Here,


A = 1 , B = -5 and C = K



Given that,


P and Q are the two zeroes of the given polynomial.

Therefore,


Product of zeroes = C/A



P × Q = -K/1 --------(1)




Sum of zeroes = -B/A



P + Q = -(-5)/1




P + Q = 5 --------(2)


And,




P-Q = 1 ---------(3)



From equation (2) we get,




P + Q = 5




P = 5-Q --------(4)



Putting the value of P in equation (3)

P - Q = 1


5-Q - Q = 1.




-2Q = 1-5



-2Q = -4



Q = -4/-2



Q = 2


Putting the value of Q in equation (4) we get,



P = 5-Q


P = 5-2 = 3




P = 3 and Q = 2



Now ,



Putting the value of P and Q in equation (1)


P × Q = - K




3 × 2 = - K



K = 6



Hence,


The value of K is 6.




HOPE IT WILL HELP YOU...... :-)

Answer 2

answer : k = 6

explanation :

P(X) = X²-5X+k

Here,

A = 1 , B = -5 and C = K

Given that,

P and Q are the two zeroes of the given polynomial.

Therefore,

Product of zeroes = C/A

P × Q = -K/1 --------(1)

Sum of zeroes = -B/A

P + Q = -(-5)/1

P + Q = 5 --------(2) And,

P-Q = 1 ---------(3)

From equation (2) we get,

P + Q = 5

P = 5-Q --------(4)

Putting the value of P in equation (3)

P - Q = 1

5-Q - Q = 1.

-2Q = 1-5

-2Q = -4

Q = -4/-2

Q = 2

Putting the value of Q in equation (4) we get,

P = 5-Q

P = 5-2 = 3

P = 3 and Q = 2

Now ,

Putting the value of P and Q in equation (1)

P × Q = - K

3 × 2 = - K

K = 6

Hence,

The value of K is 6.