>
Exams
>
Mathematics
>
Algebra
>
the number of real roots of 6 x 4 8 x 4 16
Question:
The number of real roots of
$$ (6 - x)^4 + (8 - x)^4 = 16 $$
Show Hint
When solving quartic equations, consider factoring or using substitution methods to simplify the equation.
IPU CET - 2017
IPU CET
Updated On:
Dec 11, 2025
0
2
4
6
Hide Solution
Verified By Collegedunia
The Correct Option is
D
Solution and Explanation
We solve the equation algebraically.
After solving the equation, we find that there are 6 real roots that satisfy the given equation.
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Algebra
Let the direction cosines of two lines satisfy the equations : \( 4l + m - n = 0 \) and \( 2mn + 5nl + 3lm = 0 \). Then the cosine of the acute angle between these lines is :
JEE Main - 2026
Mathematics
Algebra
View Solution
Expand \( (2x-3y)^5 \) using the Binomial Theorem.
Mizoram (MBSE) Class XII - 2026
Business Mathematics
Algebra
View Solution
Consider the 10 observations 2, 3, 5, 10, 11, 13, 15, 21, a and b such that mean of observation is a and variance is 34.2. Then the mean deviation about median, is :
JEE Main - 2026
Mathematics
Algebra
View Solution
Let \( S = \{x^3 + ax^2 + bx + c : a, b, c \in \mathbb{N} \text{ and } a, b, c \le 20\} \) be a set of polynomials. Then the number of polynomials in \( S \), which are divisible by \( x^2 + 2 \), is:
JEE Main - 2026
Mathematics
Algebra
View Solution
If \[ \sum_{r=1}^{25}\frac{r}{r^4+r^2+1}=\frac{p}{q}, \] where \(p\) and \(q\) are coprime positive integers, then \(p+q\) is equal to:
JEE Main - 2026
Mathematics
Algebra
View Solution
View More Questions
Questions Asked in IPU CET exam
The value of $\sin 20^\circ \times \sin 40^\circ \times \sin 60^\circ \times \sin 80^\circ$ is
IPU CET - 2025
Trigonometry
View Solution
The derivative of $e^{2x}\sin x$ with respect to $x$ is
IPU CET - 2025
Differentiation
View Solution
If vector $\vec{a} = 2\hat{i} + m\hat{j} + \hat{k}$ and vector $\vec{b} = \hat{i} - 2\hat{j} + 3\hat{k}$ are perpendicular to each other, then the value of $m$ is
IPU CET - 2025
Vectors
View Solution
Synonym of ``Brief'' is
IPU CET - 2025
Synonyms
View Solution
Spot the error: ``I prefer coffee than tea.''
IPU CET - 2025
Vocabulary
View Solution
View More Questions