The number of all possible positive inte...

The number of all possible positive integral values of `alpha` for which the roots of the quadratic equation `6x^2-11x+alpha=0` are rational numbers is : (a) 3 (b) 2 (c) 4 (d) 5

A

2

B

5

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:

C

Topper's Solved these Questions

JEE 2019
CENGAGE ENGLISH|Exercise Chapter 1|5 Videos
JEE 2019
CENGAGE ENGLISH|Exercise Chapter 2|7 Videos
JEE 2019
CENGAGE ENGLISH|Exercise chapter -3|1 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
CENGAGE ENGLISH|Exercise Archives (Numerical Value type)|2 Videos
LIMITS
CENGAGE ENGLISH|Exercise Comprehension Type|4 Videos

Similar Questions

Explore conceptually related problems

Number of non-negative integral values of 'k' for which roots of the equation x^(2)+6x+k=0 are rational is-

Find all the integral values of a for which the quadratic equation (x - a) (x - 10) + 1 = 0 has integral roots.

If alpha and beta are the roots of the quadratic equation x^(2) - 4x - 6 = 0 , find the values of alpha^(2) + beta^(2) .

Number of possible value(s) of integer 'a' for which the quadratic equation x^(2) + ax + 16 = 0 has integral roots, is

The number of integral values of a for which the quadratic equation (x+a)(x+1991)+1=0 has integral roots are a. 3 b. 0 c. 1 d. 2

Two different real numbers alpha and beta are the roots of the quadratic equation ax ^(2) + c=0 a,c ne 0, then alpha ^(3) + beta ^(3) is:

If [x] denotes the integral part of x and k=sin^-1 ((1+t^2)/(2t))gt0 then integral valueof alpha for which the equation (x-[k])(x+alpha)-1=0 has integral roots is (A) 1 (B) 2 (C) 4 (D) none of these

If alpha and beta are roots of the quadratic equation x ^(2) + 4x +3=0, then the equation whose roots are 2 alpha + beta and alpha + 2 beta is :

If alpha , beta , gamma are the roots of the equation x^3 -6x^2 +11 x +6=0 then sum alpha^2 beta =

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots

CENGAGE ENGLISH-JEE 2019-MCQ

Let alpha and beta be two roots of the equation x^(2) + 2x + 2 = 0. Th...
Text Solution
|
If both the roots of the quadratic equation x^(2) - mx + 4 = 0 are rea...
Text Solution
|
The number of all possible positive integral values of alpha for whic...
Text Solution
|
Consider the quadratic equation (c - 5)x^(2) - 2cx + (c - 4) = 0, c ne...
Text Solution
|
The values of lambda such that sum of the squares of the roots of the ...
Text Solution
|
If one root is cube of the other of equation 81x^2 +kx+256=0 then valu...
Text Solution
|
Let alpha and beta be the roots of the quadratic equation x^(2) sin th...
Text Solution
|
If ratio of the roots of the quadratic equation 3m^2x^2+m(m-4)x+2=0 is...
Text Solution
|
The number of integral values of m for which the quadratic expression ...
Text Solution
|
Let A={theta in (-pi /2,pi):(3+2i sin theta )/(1-2 i sin theta ) is pu...
Text Solution
|
Let Z0 is the root of equation x^2+x+1=0 and Z=3+6i(Z0)^(81)-3i(Z0)^(9...
Text Solution
|
Let z(1) and z(2) be any two non-zero complex numbers such that 3|z(1)...
Text Solution
|
If z=(sqrt(3)/2+i/2)^5+(sqrt(3)/2-i/2)^5 , then prove that Im(z)=0
Text Solution
|
Let (-2 -1/3 i)^3=(x+iy)/27 (i= sqrt(-1)) where x and y are real numbe...
Text Solution
|
Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alphaepsilonR t...
Text Solution
|
Let Z(1) and Z(2) be two complex numbers satisfying |Z(1)|=9 and |Z(2)...
Text Solution
|
Consider the statement : " P(n) : n^(2)-n+41 is prime." Then, which on...
Text Solution
|
If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , the...
Text Solution
|
Let a1, a2,...,a30 be an AP, S=sum(i=1)^(30)ai and T=sum(i=1)^(15)a(2i...
Text Solution
|
The sum of series 1+6+(9(1^(2)+2^(2)+3^(2)))/(7) + (12(1^(2)+2^(2)+...
Text Solution
|