Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi

Question

Download Solution PDF

If x2 + 2ax + 10 - 3a > 0 for all x ∈ R, then

This question was previously asked in
NIMCET 2014 Official Paper
Download PDF Attempt Online
View all NIMCET Papers >
  1. - 5 < a < 2
  2. a < -5
  3. a > 5
  4. 2 < a < 5

Answer (Detailed Solution Below)

Option 1 : - 5 < a < 2
Free Tests
View all Free tests >
Free
NIMCET 2020 Official Paper
10.5 K Users
120 Questions 480 Marks 120 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

ax2 + bx + c > 0 for all x ∈ R if: a > 0 and b2 - 4ac < 0

Calculation:

Equation x2 + 2ax + 10 - 3a > 0 for all x ∈ R

⇒ (2a)2 - [4 × (10 - 3a)] < 0 

⇒ 4a2 - [40 - 12a] < 0

⇒ 4a2 + 12a - 40 < 0

⇒ a2 + 3a - 10 < 0

⇒ (a + 5)(a - 2) < 0 

∴  -5 < a < 2

Download Solution PDF
Latest NIMCET Updates

Last updated on Jun 2, 2025

-> NIMCET 2025 admit card will be declared on June 3, 2025. Candidates can download the hall ticket till June 8, 2025.

-> NIMCET 2025 exam is scheduled for June 8, 2025. It will be conducted in Computer-Based Test (CBT) mode and will consist of 120 multiple-choice questions.

-> NIMCET 2025 results will be declared on June 27, 2025.

-> Check NIMCET 2025 previous year papers to know the exam pattern and improve your preparation.

More Quadratic Equations Questions

Q1.If the equations 2x2 + kx - 5 = 0 and x2 - 3x - 4 = 0 have one root common, then find the value of k.
Q2.If α, β are the roots of the equation x2 + 2x + 4 = 0, then find the value of \(\rm \frac{1}{\alpha^3}+\frac{1}{\beta^3}\):
Q3.If \(e^{\left(\cos ^2 x+\cos ^4 x+\cos ^6 x+\ldots \infty\right) \log _c 2}\) satisfies the equation t2 – 9t + 8 = 0, then the value of 2sin x/(sin x + √3cos x) 0 < x < π/2 is:
Q4.Let p and q be two positive number such that p + q = 2 and p4 + q4 = 272. Then p and q are roots of the equation:
Q5.Let α and β are two real roots of the equation (k + 1) tan2 x − √2 λ tan x = 1 − k, where (k ≠ −1) and are real numbers. If tan2(α + β) = 50, then value of λ is
Q6.If α, β, γ, δ are the roots of the equation x4 + x3 + x2 + x + 1 = 0, then α2021 + β2021 + γ2021 + δ2021 is equal to
Q7.If 2 and 6 are the roots of the equation ax2 + bx + 1 = 0, then the quadratic equation, whose roots are \(\frac{1}{2a+b}\) and \(\frac{1}{6a+b}\), is:
Q8.Let r and c be real numbers. If r and –r are roots of 5x3 + cx2 – 10x + 9 = 0, then c equals
Q9.A quadratic equation x2 + bx + c = 0 has two real roots. If the difference between the reciprocals of the roots is \(\frac{1}{3}\), and the sum of the reciprocals of the squares of the roots is \(\frac{5}{9}\), then the largest possible value of (b + c) is
Q10.The sum of all possible values of x satisfying the equation \(\rm 2^{4x^2}-2^{2x^2+x+16}+2^{2x+30}=0\) is
Suggested Test Series
View All >
NIMCET Previous Year Papers Mock Test
8 Total Tests with 1 Free Tests
Start Free Test
Suggested Exams
Exam-Logo
NIMCET

NIMCET Important Links

More Mathematics Questions

Q1.log10 10000 = _______?
Q2.Consider a system equation \(2x+y-z=0\), \(4x - py + 4z = 4\) and \(x-y+z=q\) where \(p, q \in I\) and \(p, q \in [1, 10]\), then identify the correct statement(s).   List-I List-II (I) Number of ordered pairs \((p, q)\) for which system of equation has unique solution is (P) 1 (II) Number of ordered pairs \((p, q)\) for which system of equation has no solution is (Q) 9 (III) Number of ordered pairs \((p, q)\) for which system of equation has infinite solution is (R) 91 (IV) Number of ordered pairs \((p, q)\) for which system of equation has atleast one solution is (S) 90
Q3.Match List I with List II:   List - I List - II (I) The number of solutions of the equation\((1 - \cos 2x)(\cos 2x + \cot^2 x) = 0\) where \(0 \le x \le 2\pi\) is (P) 4 (II) \(\tan 81^\circ - \tan 63^\circ - \tan 27^\circ + \tan 9^\circ\) equals (Q) 3 (III) The number of solutions of (x, y), which satisfy |y| = sin x and y = cos-1(cos x), where -2π ≤ x ≤ 2π is (R) 2 (IV) For the equation \(\cos^{-1}x + \cos^{-1}2x + \pi = 0\), the number of real solutions is (S) 1     (T) 0  
Q4.If Σn = 36, find n
Q5.If log 2 = 0.2614, log 3 = 0.3521, log 6 = ?
Q6.The growth model for a population is Nt = N0ert where Nt is the population at time t, N0 is the initial population and r is the per capita growth rate. How long does it take for the population numbers to double?
Q7.Suppose that the growth rate of the number of individuals (N) in a population in an environment with a carrying capacity K is modelled as \(\frac{d N}{d t}=r N \frac{K-N}{K}\) where r is the per capita growth rate and t is time; r and K are positive constants. At which of the following values of N will the population growth rate be the maximum?
Q8.The shadow of a vertical pole, formed due to a nearby lamp which is at a height of 12 m, measures 4 m. If the lamp is moved horizontally 2 m further away from the pole, the length of the shadow measures 8 m. What is the height (in m) of the pole?
Q9.A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Out of these 16 number of cards, two cards are drawn at random. Find the probability that at least one of them is an ace :
Q10.If the equations 2x2 + kx - 5 = 0 and x2 - 3x - 4 = 0 have one root common, then find the value of k.
Important Exams
Super Coaching
Exams
Test Series
Previous Year Papers
Objective Questions
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti gold old version teen patti chart all teen patti master teen patti stars