Help Needed

I was doing problems when I encountered this: IIT-JEE adv. 201 paper-II problem no. 50 (maths), I think the answer should be a) but answer given is d) , share your thoughts and help me please. :)

paper here :)

Note by Brilliant Member
1 year, 3 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Q: The The quadratic equation \(f\left( x \right) =0\) with real coefficients has purely imaginary roots. Then the equation \(f\left( f\left( x \right) \right) =0\) has

(A) only purely imaginary roots

(B) all real roots

(C) two real and two purely imaginary roots

(D) neither real nor purely imaginary roots

Answer Let \(f\left( x \right) =a{ x }^{ 2 }+c\) Where \(a\) and \(c\) are Real and \(\alpha i\) and \(-\alpha i\) be the roots of the given equation.

we can write from above equation that \(f\left( \alpha i \right) =f\left( -\alpha i \right) =0\)

We need to find the roots of \(f\left( f\left( x \right) \right) =0\)

For \(f\left( f\left( x \right) \right) =0\), \(f\left( x \right) \) Should be Purely Imaginary which gives us

\(f\left( x \right) =\alpha i=a{ x }^{ 2 }+c\) \(--------(1)\)

Case 1 : x is Purely Real

Now since a and c are Real then x cannot be real to satisfy the Equation \((1)\) => No real Roots.

Case 2 : x is Purely Imaginary

since x is purely imaginary \({ x }^{ 2 }\) is Purely Real which gives us No Imaginary Roots.

Hence the answer is \((D)\)

Rishabh Deep Singh - 1 year, 3 months ago

Log in to reply

thank you bro very much , now i think i get it :) , you are awesome :) thnx again .

Brilliant Member - 1 year, 3 months ago

Log in to reply

No problem Bro Just tag me

Rishabh Deep Singh - 1 year, 3 months ago

Log in to reply

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...