Question

Q.7 If p and q are the zeroes of the polynomial f(x) = 4x^2
-4x +1, find the value of p/q+q/p

Answer 1

P and q are the zeros of 4x² - 4x + 1 ,
so,
sum of roots = -( coefficient of x)/(coefficient of x²)
P + q = -( -4)/4 = 1
P + q = 1 --------(1)

again,
product of roots = constant/coefficient of x² = 1/4

Pq = 1/4 ----------(2)

now,
P/q + q/P = ( P² + q²)/Pq

={ (P+q)² -2Pq}/Pq

put eqns (1) and (2) value here,

= { (1)² - 2 × 1/4}/(1/4)

= (1/2)/(1/4)

= 4/2 = 2

hence ,
value of P/q + q/P = 2

Answer 2

f(x) = 4x²-4x+1
= 4x²-2x-2x+1
= 2x(2x-1)-1(2x-1)
=(2x-1)(2x-1)
It's both zeroes are co-incident
Hence p = q = 1/2
p÷q + q÷p
=1/2÷1/2 + 1/2÷1/2
=1/2×2/1 + 1/2×2/1
=1 + 1
=2