If m and n are the root of the equation x2 ax b 0 and m2 n2 are the roots of the equation x2 minus c...........

Quantitative Aptitude (CDS) Quadratic Equations

If m and n are the root of the equation x² + ax +b = 0 and m², n² are the roots of the equation x² − cx + d = 0 then which of the following is/are correct? 1. 2b − a² = c

2. b² = d

Select the correct answer using the codes given below:

only 1

only 2

both 1 and 2

neither 1 nor 2

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Explanation:

Here m and n are the roots of the equation
x² + ax + b = 0
m + n = −a … . (i)
mn = b … (ii)
m² and n² are the roots of the equation of
x² − cx + d = 0
m² + n² = c ….. (iii)
m² n² = d ….. (iv)
By squaring (i) both side, we get
m² + n² + 2mn = a²
⇒ c =a² − 2b
⇒ 2b−a² = −c
Therefore statement 1 incorrect
From (ii) m² n² = b² => b² =d
Statement 2 is correct