>
Exams
>
Engineering Mathematics
>
Algebra
>
solve the cubic equation x 3 frac 15 2 x 2 18x 20
Question:
Solve the cubic equation:
\[ x^3 - \frac{15}{2} x^2 + 18x + 20 = 0 \]
Show Hint
To solve cubic equations, you can use the Rational Root Theorem to test possible rational roots or apply synthetic division to simplify the equation.
GATE CE - 2025
GATE CE
Updated On:
Feb 17, 2025
Hide Solution
Verified By Collegedunia
Solution and Explanation
To solve this cubic equation, we can use methods such as factoring, synthetic division, or the cubic formula. The roots of the equation are the solutions.
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Algebra
Given the equation:
\[ 3^{x^2} = 27 \times 9^x \]
Find the value of:
\[ \frac{2^{x^2}}{(2^x)^2} \]
GATE DA - 2025
Engineering Mathematics
Algebra
View Solution
View All
Questions Asked in GATE CE exam
Eigenvalue question:
\[\begin{pmatrix} 6 & 8 \\ 4 & 2 \end{pmatrix} \quad \text{Eigenvalue options:} \quad \text{(i) 1, (ii) 2, (iii) 3, (iv) 4}\]
GATE CE - 2025
Linear Algebra
View Solution
Given the matrix equation:
\[A = \begin{pmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{pmatrix} \quad A \cdot X = B\]
Where \( A \) is the matrix, \( X \) is the unknown vector, and \( B \) is a constant vector. Solve for \( X \).
GATE CE - 2025
Linear Algebra
View Solution
Given the following conditions, determine the value of the 15-minute Peak Hourly Factor (PHF):
Given:
- Vehicles in the peak hour come in 10-minute intervals
- Find the value of the 15-minute PHF
GATE CE - 2025
Concept of airport runway length
View Solution
Runway length after elevation and temperature correction is 700 m. The effective gradient is 1%. Find the final corrected length.
GATE CE - 2025
Concept of airport runway length
View Solution
Match the following processes to their corresponding descriptions: Sintering, Fouling , Positioning , Coking
GATE CE - 2025
Material Science
View Solution
View More Questions