If `4a^2-4ab-c^2-2bc` has `(pa-2b-c)` as one factor then find the value of `p`

If a/2=b/3 =c/4 =(3a-ab+4c)/p , then find the value of p.

If a^2+b^2+c^2 = 25 and a+b+c=7 , then find the value of ab+bc+ca .

If a+b+c=1 , ab+bc+ca=-2 and abc=1 then find the value of a^4+b^4+c^4

Prove that |(bc-a^2, ca-b^2, ab-c^2),(ca-b^2, ab-c^2, bc-a^2),(ab-c^2, bc-a^2, ca-b^2)| is divisible by a+b+c. Also find the value of the quotient.

If A:B=3:4, B:C=5:2 then find the value of A:B:C.

If |{:(-a^2," "ab," "ac),(" "ab,-b^2," "bc),(" "ac," "bc,-c^2):}|=lambdaa^2b^2c^2, then find the value of lambda

If a^(2)-2a-3 is a factor of a^(4)+pa^(3)+12a-9 , find the value of p^(2)-2q-3 .

When a=3 , b=0 , c=-2 , then find the value of : ab+2bc+3ca+4abc.

If a+b+c=9 and ab+bc+ca=26, find the values of a^2+b^2+c^2

if [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=lambda a^2b^2c^2 then find the value of lambda