Join WhatsApp Icon CAT WhatsApp Group
Question 8

Let $$f(x) = ax^2 + bx + c$$, where a, b and c are certain constants and $$a \neq 0$$ ?

It is known that f(5) = - 3f(2). and that 3 is a root of f(x) = 0.

What is the value of a + b + c?

Solution

Share

f(3) = 9a + 3b + c = 0 f(5) = 25a + 5b + c
f(2) = 4a + 2b + c
f(5) = -3f(2) => 25a + 5b + c = -12a -6b -3c
=> 37a + 11b + 4c = 0 --> (1)
4(9a + 3b + c) = 36a + 12b + 4c = 0 --> (2)
From (1) and (2), a - b = 0 => a = b
=> c = -12a
The equation is, therefore, $$ax^2 + ax - 12a = 0 => x^2 + x - 12 = 0$$
a + b + c = a + a - 12a = -10a.
But the value of a is not given. Therefore, the value cannot be determined.

Was this solution helpful?

Get AI Help

Video Solution

video
View More Questions From Functions, Graphs and Statistics

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 41+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Probability, Combinatorics QuestionsCAT Profit and Loss QuestionsCAT Averages QuestionsCAT Coordinate Geometry QuestionsCAT Logarithms, Surds and Indices Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Quant Based DI QuestionsCAT Miscellaneous LR QuestionsCAT Charts QuestionsCAT Maxima-Minima QuestionsCAT Selection With Condition Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Para Summary QuestionsCAT Odd One Out QuestionsCAT Reading Comprehension QuestionsCAT Critical Reasoning QuestionsCAT Verbal Ability Questions

Free CAT Quant Questions

CAT Time Speed DistanceCAT MensurationCAT Linear EquationsCAT PercentagesCAT Progressions and SeriesCAT LogarithmsCAT Coordinate GeometryCAT InequalitiesCAT Simple Interest Compound InterestCAT Probability, CombinatoricsCAT Venn DiagramsCAT Logarithms, Surds and IndicesCAT Functions, Graphs and StatisticsCAT RemaindersCAT Number SystemsCAT AveragesCAT ArithmeticCAT Time And WorkCAT Profit and LossCAT Profit And LossCAT Time, Speed and DistanceCAT Number SeriesCAT AlgebraCAT Quadratic EquationsCAT Averages, Ratio and ProportionCAT Data SufficiencyCAT MiscellaneousCAT GeometryCAT Averages Mixtures Alligations

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Start your IIM journey with the right preparation and crack CAT 2026.

Enroll Now
Ask AI