Exams › IBPS PO › Quantitative Aptitude

In this question, two equations are given. Answer the question based on the given equations: I. $2x^2 - Px + 10 = 0$ $a$ and $b$ are the two roots of the equation, and their sum is $a+b=4.5$ $(a>b)$. II. $4y^2 - Ry + 19 = 0$ $c$ and $d$ are the two roots of the equation, such that one root is 40% of the largest root of the first equation. $(c>d)$ Which of the following statements is/are correct? I. $a+c=b+d$ II. $c+d=5.75$ III. $a>b>c>d$

1. Only I
2. Only III
3. Only II
4. All of these

Correct answer: Only II

Solution

From $a+b=4.5$ and $ab=10/2=5$, the roots are $4$ and $0.5$, so $a=4$ and $b=0.5$. One root of the second equation is 40% of the largest root of the first equation, i.e. $0.4\times 4=1.6$; using the product $cd=19/4=4.75$, the other root is $2.96875$, giving $c+d=5.75$. Thus only statement II is correct.

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