# What are we learning ?

**Competency in Focus:**Discriminant of the quadratic equation and basic inequalities This problem from I.S.I. B.Stat. Entrance 2017 is a problem on quadratic equation and some basic inequalities .

# First look at the knowledge graph.

# Next understand the problem

Let a , b , c be real numbers such that a+b+c<0. Suppose that equation \( ax^2+bx+c=0 \) has imaginary roots .Then ,

##### Source of the problem

I.S.I. B.Stat. Entrance 2016, UGA Problem 26

##### Key Competency

Discriminant of the quadratic equation and basic inequalities

##### Difficulty Level

6/10

##### Suggested Book

Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics

# Start with hints

Do you really need a hint? Try it first!

Given that the quadratic equation \( ax^2+bx+c=0\) has imaginary roots then what can we say about it’s discriminant ?

Discriminant of the quadratic equation having imaginary roots is less than zero . So, we have

So have same sign.

So have same sign.

Also,

, as . Now we will check the options.

, as . Now we will check the options.

This shows, if then , contradicting . Hence .

# Similar Problems

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