#### Thank you for registering.

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

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0
MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

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

Jitender Singh IIT Delhi
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