- Trending Categories
- Data Structure
- Operating System
- C Programming
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
If the zeroes of the polynomial $x^3 - 3x^2 + x + 1$ are $a-b, a, a + b$, find $a$ and $b$.
The zeroes of the polynomial $x^3 - 3x^2 + x + 1$ are $a-b, a, a + b$.
We have to find $a$ and $b$.
Let $\alpha, \beta$ and $\gamma$ be the zeroes of polynomial $x^3 – 3x^2 + x + 1$.
$\alpha = a-b, \beta = a$ and $\gamma = a + b$.
Sum of zeroes $= \alpha + \beta + \gamma$
$(a – b) + a + (a + b)=3$
$a-b + a + a + b = 3$
$3a = 3$
Product of zeroes $= \alpha \beta \gamma$
$(a – b) a (a + b) = -1$
$(a^2 – b^2)a = -1$
$a^3 – ab^2 = -1$...… (ii)
Putting the value of $a$ from equation (i) in equation (ii), we have,
$(1)^3-(1)b^2 = -1$
$1 – b^2 = -1$
$b^2 = 1 + 1$
$b^2 = 2$
$b = \pm \sqrt2$
Hence, $a = 1$ and $b = \pm \sqrt2$
- Find FIRST & FOLLOW for the following Grammar. S → A a A | B b B A → b B B → ε
- Find multiple of x closest to or a ^ b (a raised to power b) in C++
- Show that the following grammar is LR (1) S → A a |b A c |B c | b B a A → d B → d
- Minimum positive integer value possible of X for given A and B in X = P*A + Q*B in C++
- Find 2^(2^A) % B in C++
- Construct SLR (1) parsing table for the following grammar S → x A y |x B y |x A z A → q s | q B → q
- Find minimum positive integer x such that a(x^2) + b(x) + c >= k in C++
- Count number of triplets (a, b, c) such that a^2 + b^2 = c^2 and 1<=a<=b<=c<= n in C++
- Print values of ‘a’ in equation (a+b) <= n and a+b is divisible by x
- Check if a + b = c is valid after removing all zeroes from a, b and c in C++
- Find the multiple of x which is closest to a^b in C++
- Sum of the Series 1 + x/1 + x^2/2 + x^3/3 + .. + x^n/n in C++
- Larger of a^b or b^a in C++
- Python a += b is not always a = a + b
- Construct a Finite Automata for the regular expression ((a+b)(a+b))*.
- Count pairs (a, b) whose sum of cubes is N (a^3 + b^3 = N) in C++