If p, q, r be real, then the intervals in which, `f(x)=|(x+p^2,pq,pr),(pq,x+q^2,qr),(pr,qr,x+r^2)|`

If p, q, r be real then the intervals in which, f(x)=|(x+q^(2),pq,pr),(pq,x+p^(2),qr),(pr,qr,x+r^(2))|

if p,q,r be real then the interval in which f(x) =|underset(pr" "qr" "x+r^(2))underset(pq" "x+q^(2)" "qr)(x+p^(2)" "pq" "pr)|,

Prove that |{:(p^(2)+1,pq,pr),(pq,q^(2)+1,qr),(pr,qr,r^(2)+1):}|=1+p^(2)+q^(2)+r^(2)

If p = 4,q = 3 and r = -2, find the values of : (3pq+2qr^(2))/(p+q-r)

If pq + qr + rp = 0 , then what is the value of (p^(2))/(p^(2) - qr) + (q^(2))/(q^(2) - rp) + (r^(2))/(r^(2) - pq) ?

If p:q=3:4 and q:r=8:9 then p:r is

If p = 4, q= 3 and r = -2, find the values of : (p^(2)+q^(2)-r^(2))/(pq+qr-pr)

If p = 3 , q = 2 and r = -1, find the values of (3p^(2)q+5r)/(2pq-3qr)

If p, q, r are the roots of the equation x^3 -3x^2 + 3x = 0 , then the value of |[qr-p^2, r^2 , q^2],[r^2,pr-q^2,p^2],[q^2,p^2,pq-r^2]|=