×

#### 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
```
let – 1≤ p ≤1 .Show that the equation 4x 3 -3x-p=0 has a unique root in the interval [-1/2, 1] and identify it. Ans: x= cos {1/3 cos -1 (p)}
let – 1≤ p ≤1 .Show that the equation 4x3-3x-p=0 has a unique root in the interval [-1/2, 1] and identify it. Ans: x= cos {1/3 cos-1(p)}

```
4 years ago

Vikas TU
14149 Points
```							First find f(-0.5) and f(1) in terms of p.And suit the domain for p lyng in [-1,1]and check relation in  f(-0.5) and f(1).Next step is to proove the function is continuous and differntiable.I would be and then apply Mean Value theorem to it. simply.
```
4 years ago
Ajay
209 Points
```							Firstly the question is wrong , the interval in which root will be unique is [1/2, 1] instead of [-1/2, 1].The equation can be written as 4x3-3x  = pDraw the graph of of function y = f(x) = 4x3-3x. by finding its maxima and minima.The given equation will have unique root in any interval if line y = p cuts the graph y=f(x) at exactly one point.From the graph it would be clear that that this will be true if interval of x  is [1/2, 1] Let the root be a, so it will satisfy the given equation we have4a3-3a = plet a = cosr4cos3r-3cosr = pcos3r = pr  = 1/3cos-1pa = cosr = cos(1/3cos-1p) will be the required root
```
4 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »

### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution

### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions