(C) Given the cubic equation: $x^3+4x^2-9x-36=0$Factorizing the equation:$x^2(x+4)-9(x+4)=0$$(x^2-9)(x+4)=0$$(x-3)(x+3)(x+4)=0$The roots are $x = -4,

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) Given the cubic equation: $x^3+4x^2-9x-36=0$Factorizing the equation:$x^2(x+4)-9(x+4)=0$$(x^2-9)(x+4)=0$$(x-3)(x+3)(x+4)=0$The roots are $x = -4, -3, 3$.Given the condition $\alpha Now,calculate $\alpha+2\beta+3\gamma$:$\alpha+2\beta+3\gamma = -4 + 2(-3) + 3(3)$$= -4 - 6 + 9$$= -10 + 9 = -1$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

Easy

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4x^2-9x-36=0$ and $\alpha < \beta < \gamma$,then find the value of $\alpha+2\beta+3\gamma$.

TS EAMCET 2023 All TS EAMCET

A
$1$
B
$0$
C
$-1$
D
$-2$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-2.Quadratic Equations and Inequations

Subtopic

Solution of quadratic equations and Nature of roots

Previous Year

TS EAMCET 2023 Paper All TS EAMCET years →

The solution to the equation $4^{(x^2 + 2)} - 9 \cdot 2^{(x^2 + 2)} + 8 = 0$ is:

Difficult

View Solution

If the roots of the equation $(b - c)x^2 + (c - a)x + (a - b) = 0$ are equal,then $a, b, c$ are in which progression?

Medium

View Solution

Let $[x]$ denote the greatest integer less than or equal to $x$. Then,the values of $x \in \mathbb{R}$ satisfying the equation $[e^{x}]^{2} + [e^{x} + 1] - 3 = 0$ lie in the interval:

DifficultJEE MAIN 2021

View Solution

The integral values of $a$ for which the quadratic equation $(x - a)(x - 10) + 1 = 0$ has integral roots are

View Solution

Let $\alpha, \beta, \gamma, \delta$ be the roots of the equation $x^4 + x^2 + 1 = 0$. Then the equation whose roots are $\alpha^2, \beta^2, \gamma^2, \delta^2$ is:

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4x^2-9x-36=0$ and $\alpha < \beta < \gamma$,then find the value of $\alpha+2\beta+3\gamma$.

Similar Questions

The solution to the equation $4^{(x^2 + 2)} - 9 \cdot 2^{(x^2 + 2)} + 8 = 0$ is:

If the roots of the equation $(b - c)x^2 + (c - a)x + (a - b) = 0$ are equal,then $a, b, c$ are in which progression?

Let $[x]$ denote the greatest integer less than or equal to $x$. Then,the values of $x \in \mathbb{R}$ satisfying the equation $[e^{x}]^{2} + [e^{x} + 1] - 3 = 0$ lie in the interval:

The integral values of $a$ for which the quadratic equation $(x - a)(x - 10) + 1 = 0$ has integral roots are

Let $\alpha, \beta, \gamma, \delta$ be the roots of the equation $x^4 + x^2 + 1 = 0$. Then the equation whose roots are $\alpha^2, \beta^2, \gamma^2, \delta^2$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module