How many solutions the following equation has?3x3=x2+18x+32x2-18x-32-4x2

Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

How many solutions the following equation has?

$3 x^{3} = (x^{2} + \sqrt{18} x + \sqrt{32}) (x^{2} - \sqrt{18} x - \sqrt{32}) - 4 x^{2}$

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

Four

two

no solution

None

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given equation is,

3 x^{3} = (x^{2} + \sqrt{18} x + \sqrt{32}) (x^{2} - \sqrt{18} x - \sqrt{32}) - 4 x^{2}

Solve it as,

3 x^{3} = (x^{2} + \sqrt{18} x + \sqrt{32}) (x^{2} - \sqrt{18} x - \sqrt{32}) - 4 x^{2}

3 x^{3} = (x^{4} - (\sqrt{18} x + \sqrt{32})^{2}) - 4 x^{2}

[Since

(a - b) (a + b) = (a^{2} - b^{2})]

3 x^{3} = (x^{4} - (18 x^{2} + 32 + 2 \sqrt{18} \sqrt{32} x)) - 4 x^{2}

[Since

{(a + b)}^{2} = a^{2} + b^{2} + 2 ab]

3 x^{3} = x^{4} - 18 x^{2} - 32 - 2 \sqrt{18} \sqrt{32} x - 4 x^{2}

x^{4} - 3 x^{3} - 22 x^{2} - 2 \sqrt{18} \sqrt{32} x - 32 = 0

x^{4} - 3 x^{3} - 22 x^{2} - 48 x - 32 =

0
The highest power of variable in the above equation is 4, so its degree will be 4.
Now the degree of a polynomial is equal to the number of solutions of the polynomial.
Thus, the number of solutions of the equation

3 x^{3} = (x^{2} + \sqrt{18} x + \sqrt{32}) (x^{2} - \sqrt{18} x - \sqrt{32}) - 4 x^{2}

= 4.
So, the correct option is 1.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE