Bodhee Prep-CAT Online Preparation

CAT 2019 Quant Question with Solution 46

The quadratic equation $x^{2}+b x+c=0$ has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of $b^{2}+c$ ?

  1. 3721
  2. 549
  3. 427
  4. 361
Show Answer

Correct Answer: Option: 2

Sum of roots = 4a+3a=7a=-b

Or b=-7a

Product of roots = 4a×3a =c

Or $c=12{{a}^{2}}$

Now, ${{b}^{2}}+c={{(-7a)}^{2}}+12{{a}^{2}}=61{{a}^{2}}$

Comparing the options.

Option 1: $61{{a}^{2}}=3721$ $\Rightarrow {{a}^{2}}=61$, clearly a is not an integer.

Option 2: $61{{a}^{2}}=549$ $\Rightarrow {{a}^{2}}=9$, we can have a =-3 or 3 (an integer)

Option 3: $61{{a}^{2}}=427$ $\Rightarrow {{a}^{2}}=7$, clearly a is not an integer.

Option 4: $61{{a}^{2}}=361$ $\Rightarrow {{a}^{2}}=\frac{361}{61}$, clearly a is not an integer.

CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2019 Slot-1

CAT 2019 Slot-2

CAT 2023
Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon