Question:
If the roots \(x^2 + ax + 9 = 0\) are complex, then
If the roots \(x^2 + ax + 9 = 0\) are complex, then
Show Hint
For complex roots: discriminant must be negative.
Updated On: Apr 15, 2026
- \(a<6\)
- \(a<-6\)
- \(|a|<6\)
- \(|a|>6\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
Complex roots when discriminant \( < 0 \).
Step 1: Discriminant.
\[ D = a^2 - 36 < 0 \] \[ a^2 < 36 \Rightarrow |a| < 6 \]
Step 1: Discriminant.
\[ D = a^2 - 36 < 0 \] \[ a^2 < 36 \Rightarrow |a| < 6 \]
Was this answer helpful?
0
0
Top MET Mathematics Questions
- Let \( f:\mathbb{N} \to \mathbb{N} \) be defined as \[ f(n)= \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] Then \( f \) is:
- MET - 2024
- Mathematics
- types of functions
- Given vectors \(\vec{a}, \vec{b}, \vec{c}\) are non-collinear and \((\vec{a}+\vec{b})\) is collinear with \((\vec{b}+\vec{c})\) which is collinear with \(\vec{a}\), and \(|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}\), find \(|\vec{a}+\vec{b}+\vec{c}|\).
- MET - 2024
- Mathematics
- Addition of Vectors
- Given \(\frac{dy}{dx} + 2y\tan x = \sin x\), \(y=0\) at \(x=\frac{\pi}{3}\). If maximum value of \(y\) is \(1/k\), find \(k\).
- MET - 2024
- Mathematics
- Differential equations
- If \(x = \sin(2\tan^{-1}2)\), \(y = \sin\left(\frac{1}{2}\tan^{-1}\frac{4}{3}\right)\), then:
- MET - 2024
- Mathematics
- Properties of Inverse Trigonometric Functions
- Let \( D = \begin{vmatrix} n & n^2 & n^3 \\ n^2 & n^3 & n^5 \\ 1 & 2 & 3 \end{vmatrix} \). Then \( \lim_{n \to \infty} \frac{M_{11} + C_{33}}{(M_{13})^2} \) is:
- MET - 2024
- Mathematics
- Determinants
View More Questions
Top MET Complex Numbers and Quadratic Equations Questions
- If \(\alpha\) and \(\beta\) are roots of \(4x^2 + 3x + 7 = 0\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is
- MET - 2021
- Mathematics
- Complex Numbers and Quadratic Equations
- The equation \((\cos p - 1)x^2 + \cos p \, x + \sin p = 0\) has real roots. Then \(p\) lies in
- MET - 2021
- Mathematics
- Complex Numbers and Quadratic Equations
- The quadratic equation whose roots are \(\frac{1}{3+\sqrt{2}}\) and \(\frac{1}{3-\sqrt{2}}\), will be:
- MET - 2020
- Mathematics
- Complex Numbers and Quadratic Equations
- The sum of the real solutions of equation \(2|x|^2 + 51 = |1 + 20x|\) is
- MET - 2020
- Mathematics
- Complex Numbers and Quadratic Equations
- Let \( f(x) = x^{2} + ax + b \), where \( a, b \in \mathbb{R} \). If \( f(x)=0 \) has all its roots imaginary, then the roots of \( f(x) + f'(x) + f''(x) = 0 \) are
- MET - 2009
- Mathematics
- Complex Numbers and Quadratic Equations
View More Questions
Top MET Questions
- Let \( f:\mathbb{N} \to \mathbb{N} \) be defined as \[ f(n)= \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] Then \( f \) is:
- MET - 2024
- types of functions
- Given vectors \(\vec{a}, \vec{b}, \vec{c}\) are non-collinear and \((\vec{a}+\vec{b})\) is collinear with \((\vec{b}+\vec{c})\) which is collinear with \(\vec{a}\), and \(|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}\), find \(|\vec{a}+\vec{b}+\vec{c}|\).
- MET - 2024
- Addition of Vectors
- Given \(\frac{dy}{dx} + 2y\tan x = \sin x\), \(y=0\) at \(x=\frac{\pi}{3}\). If maximum value of \(y\) is \(1/k\), find \(k\).
- MET - 2024
- Differential equations
- Let \( f(x) \) be a polynomial such that \( f(x) + f(1/x) = f(x)f(1/x) \), \( x > 0 \). If \( \int f(x)\,dx = g(x) + c \) and \( g(1) = \frac{4}{3} \), \( f(3) = 10 \), then \( g(3) \) is:
- MET - 2024
- Definite Integral
- A real differentiable function \(f\) satisfies \(f(x)+f(y)+2xy=f(x+y)\). Given \(f''(0)=0\), then \[ \int_0^{\pi/2} f(\sin x)\,dx = \]
- MET - 2024
- Definite Integral
View More Questions