Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
Close
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

⇐ BackProceed to Checkout ⇒
There are no items in this cart.
Continue Shopping

show that the equation x 4 +4x 3 -4x-13=0 has two real roots and two imaginary roots.











show that the equation x4+4x3-4x-13=0 has two real roots and two imaginary roots.









      


Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
f(x) = x^{4} +4x^{3}-4x-13 = 0
f(1) = 1^{4} +4.1^{3}-4.1-13 = -12
f(2) = 2^{4} +4.2^{3}-4.2-13 = 27
→There is one root lie b/w (1, 2)
f(-3) = (-3)^{4} +4.(-3)^{3}-4.(-3)-13 = -28
f(-4) = (-4)^{4} +4.(-4)^{3}-4.(-4)-13 = 3
→There is another root lie b/w (3, 4) which is close to 4.
-> There is no other inteval like this in which f(x) changes its sign.
-> So the other two roots are imaginary.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Register ICAT

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More