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If \( m\) and \( n\) are the roots of the equation \( x^{2}\) +\( ax\) + \( b\) = \( 0\), and \( m^{2}\) and \( n^{2}\) are the roots of the equation \( x^{2}\) - \( cx\) +\( d\) = \( 0\), then which of the following is/are correct?
1.\( 2b\) - \( a^{2}\) = \( c\)
2.\( b^{2}\)= \( d\)
Select the coorect answer using the code given below :

A) 1 only
B) 2 only
C) Both 1 and 2
D) Neither 1 nor 2

Correct Answer:


B) 2 only

Description for Correct answer:
According to question m and n are roots of equation,

\( \Large x^{2}+ax+b =0 \)

m+n = -a

and mn = b ... (i)

Now \( \Large m^{2} and n^{2} \) are the root of equation

\( \Large x^{2}-cx+d =0 \)

\( \Large m^{2} + n^{2} =c \)

and \( \Large m^{2} n^{2} =d \) ... (ii)

Now \( \Large (an + n)^{2} \) = \( \Large m^{2} + n^{2} + 2mn \)

\( \Large (-a)^{2} = c + 2b \)

\( \Large a^{2} = c + 2b + 2b - c\)

Conclusion (i) is wrong

Now mn = b

\( \Large m^{2}n^{2} = b^{2} = d \)

\( \Large b^{2} = d \)

Conclusion (ii) is correct

Option (B)is true.

Part of solved CDS Maths(1) questions and answers : Exams >> CDSE >> CDS Maths(1)

Comments

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