Question:
If \( a \) and \( a^2 \) are the roots of \( x^2 - 6x + c = 0 \), then the positive value of \( c \) is
If \( a \) and \( a^2 \) are the roots of \( x^2 - 6x + c = 0 \), then the positive value of \( c \) is
Show Hint
Always check both roots when solving quadratic-based parameter problems.
Updated On: May 2, 2026
- \(2\)
- \(3\)
- \(4\)
- \(9\)
- \(8\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
\[
\alpha + \beta = 6, \quad \alpha\beta = c
\]
Step 1: Use sum of roots.
\[ a + a^2 = 6 \Rightarrow a^2 + a - 6 = 0 \]
Step 2: Solve for \( a \).
\[ a = 2 \text{ or } -3 \]
Step 3: Find \( c \).
\[ c = a \cdot a^2 = a^3 \] For \( a=2 \Rightarrow c=8 \)
For \( a=-3 \Rightarrow c=-27 \) Positive value: \[ c = 8 \]
Step 1: Use sum of roots.
\[ a + a^2 = 6 \Rightarrow a^2 + a - 6 = 0 \]
Step 2: Solve for \( a \).
\[ a = 2 \text{ or } -3 \]
Step 3: Find \( c \).
\[ c = a \cdot a^2 = a^3 \] For \( a=2 \Rightarrow c=8 \)
For \( a=-3 \Rightarrow c=-27 \) Positive value: \[ c = 8 \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Complex Numbers and Quadratic Equations Questions
- Let $x = 2$ be a root of $y = 4x^2 - 14x + q = 0$. Then $y$ is equal to
- The value of $ \frac{\cos 30{}^\circ +i\sin 30{}^\circ }{\cos 60{}^\circ -i\sin 60{}^\circ } $ is equal to
- The value of $\sum\limits^{n}_{k=0}\left(i^{k}+i^{k+1}\right)$, where $i^2 = -1$, is equal to
- The value of The value of $\frac{2(\cos \, 75^{\circ} + i \, \sin \, 75^{\circ})}{0.2(\cos \, 30^{\circ} + i \, \sin \, 30^{\circ})}$ is
- If $ {{(\sqrt{5}+\sqrt{3}i)}^{33}}={{2}^{49}}z, $ then modulus of the complex number $z$ is equal to
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions