Discriminant question Find the values of \(\displaystyle\lambda\) for

Leia Sullivan

Leia Sullivan

Answered question

2022-04-13

Discriminant question
Find the values of λ for which 4a210ab+10b2+λ(3a210ab+3b2) is a perfect square.

Answer & Explanation

lildeutsch11xq2j

lildeutsch11xq2j

Beginner2022-04-14Added 13 answers

What you did is fine. Now, note that
D4=b2(25(1+λ)2(4+3λ)(10+3λ)).
So, solve the quadratic equation
25(1+λ)2=(4+3λ)(10+3λ);
you will get that λ=54 or that λ=34.

gil001q4wq

gil001q4wq

Beginner2022-04-15Added 11 answers

Taking your expression about a, it's determinant must be 0.
So we have D=(10b(1+λ))24b2(4+3λ)(10+3λ)

=b2(100(1+λ)24(4+3λ)(10+3λ))

=b2(64λ2+32λ60)

=4b2(16λ2+8λ15)

=4b2(4λ3)(4λ+5)

=0.

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