Suppose a,b in R. If the equation x^(2)-...

Suppose a,b `in` R. If the equation `x^(2)-(2a+b)x+(2a^(2)+b^(2)-b+1//2)=0` has two real roots, then

`a = (1)/(2), b = - 1`

`a = - (1)/(2), b =1`

`a = 2, b = 1`

`a = - 2, b = - 1`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

QUADRATIC EQUATIONS
MCGROW HILL PUBLICATION|Exercise Solved Examples (Level 2 (Straight Objective Type Questions))|21 Videos
QUADRATIC EQUATIONS
MCGROW HILL PUBLICATION|Exercise Solved Examples (Numerical Answer Type Questions)|18 Videos
QUADRATIC EQUATIONS
MCGROW HILL PUBLICATION|Exercise Questions from previous Years. B - architecture entrance examination papers|16 Videos
PROGRESSIONS
MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|25 Videos
SETS, RELATIONS AND FUNCTIONS
MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEAR.S B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|19 Videos

Similar Questions

Explore conceptually related problems

Show that the equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 has no real roots,when a!=b

If the roots of the equation x^(2)+2cx+ab=0 are real unequal,prove that the equation x^(2)-2(a+b)x+a^(2)+b^(2)+2c^(2)=0 has no real roots.

Suppose a, b, c are real numbers, and each of the equations x^(2)+2ax+b^(2)=0 and x^(2)+2bx+c^(2)=0 has two distinct real roots. Then the equation x^(2)+2cx+a^(2)=0 has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots

If a,b,c,d in R, then the equation (x^(2)+ax-3b)(x^(2)-cx+b)(x^(2)-dx+2b)=0 has a.6 real roots b.at least 2 real roots c.4 real roots d.none of these

If a, b in R , and the equation x^(2) + (a - b) x - a - b + 1 = 0 has real roots for all b in R , then a lies in the in terval

If a and b are positive real numbers and each of the equations x^(2)+3ax+b=0 and x^(2)+bx+3a=0 has real roots,then the smallest value of (a+b) is

If a,b in R and the equation x^(2)+(a-b)x+1-a-b=0 has unequal roots for all b in R then a can be

If a and b are positive numbers and eah of the equations x^(2)+ax+2b=0 and x^(2)+2bx+a=0 has real roots,then the smallest possible value of (a+b) is

If the equation x^(2)+a^(2)x+b^(2)=0 has two roots each of which exceeds a number c,then

If a,b,c in R and the quadratic equation x^(2)+(a+b)x+c=0 has no real roots then

MCGROW HILL PUBLICATION-QUADRATIC EQUATIONS-Solved Examples (Level 1 ( Single Correct Answer Type Questions)

If a, b are two real number satisfying the relation 2a^(2) - 3a - 1 =...
Text Solution
|
If alpha, beta are roots of x^(2)-2x-1=0, then value of 5alpha^(4)+12b...
Text Solution
|
Suppose a, b, c are the lengths of three sides of a Delta ABC , a gt b...
Text Solution
|
A root of the equation (a + b)(ax + b)(a - bx) = (a^2x - b^2)(a + bx) ...
Text Solution
|
Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...
Text Solution
|
Suppose a, b, in R . If the roots of x^(2) - ax + b = 0 are real and d...
Text Solution
|
If a is the minimum root of the equation x^(2) - 3|x|- 2 = 0 , then va...
Text Solution
|
Let f(x) = (x^(2) - 2x + 3)/( x^(2) - 2x - 8) , x in R - {-2, 4} The r...
Text Solution
|
Suppose a, b, care three non-zero real numbers. The equation x^2+(a+b+...
Text Solution
|
Suppose a,b in R. If the equation x^(2)-(2a+b)x+(2a^(2)+b^(2)-b+1//2)=...
Text Solution
|
The equation e^(sinx)-e^(-sinx)-4=0 has (A) infinite number of real ro...
Text Solution
|
If x^(2) - 3x + 2 is a factor of x^(4) - ax^(2) + b then the equatio...
Text Solution
|
Let for a != a1 != 0 , f(x)=ax^2+bx+c ,g(x)=a1x^2+b1x+c1 and p(x) = f(...
Text Solution
|
If a + b + c = 0 and a ne c then the roots of the equation (b + c - a)...
Text Solution
|
if alpha&betaare the roots of the quadratic equation ax^2 + bx + c = 0...
Text Solution
|
If 3p^(2)=5p+2 and 3q^(2)=5q+2 then the equation whose roots 3p-2p an...
Text Solution
|
The number of real roots of (x+3)^4+(x+5)^4=16
Text Solution
|
If a, b, c in R and the quadratic equation x^2 + (a + b) x + c = ...
Text Solution
|
The value of 6+ log(3//2) (1/(3sqrt2)sqrt(4-1/(3sqrt2)sqrt(4-1/(3sq...
Text Solution
|
The sum of the roots of the equation x + 1 - 2 log(2) (2^(x) + 3) + 2 ...
Text Solution
|