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the condition that x^4 + ax^3 bx^2 + cx + d is a perfect square,is A)c^2=ad B)c^2=ad^2 C)c^2=(ad)^2 D)c^2=(a^2) *d plzz illustrate the answer...

the condition that x^4 + ax^3 bx^2 + cx + d is a perfect square,is


A)c^2=ad


B)c^2=ad^2


C)c^2=(ad)^2


D)c^2=(a^2) *d


plzz illustrate the answer...

Grade:12

3 Answers

DIVYANK GUPTA
15 Points
10 years ago

the answer is c^2=a^2*d.Hints:compare the given biquardratic with the square of an quardratic (for eg(px^2 +qx+r)^2).Equate the coefficients of the corresponding power of x.u will get p=1 ;c=2qr;d=r^2 and a=2q ;now use these relations to get the ans

 

shyam sundar
36 Points
10 years ago

the answer is c^2=a^2*d.Hints:compare the given biquardratic with the square of an quardratic (for eg(px^2 +qx+r)^2).Equate the coefficients of the corresponding power of x.u will get p=1 ;c=2qr;d=r^2 and a=2q ;now use these relations to get the ans

AAYUSH KESHAVA
22 Points
9 years ago

let x^4 + ax^3 bx^2 + cx + d =(px^2+qx+k)^2

                                            =p^2 x^4+q^2 x^2+k^2+2pqx^3+2kqx+2pkx^2

                                            =p^2 x^4+2pqx^3+x^2(q^2+2pk)+2kqx+k^2.

now just compare the constants of lhs and rhs and try to hunt the answer.

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