Home
Class 12
MATHS
If a, b in R and ax^2 + bx +6 = 0,a!= 0 ...

If `a, b in R` and `ax^2 + bx +6 = 0,a!= 0` does not have two distinct real roots, then :

A

(a) minimum possible value of `3a+b` is `-2`

B

(b) minimum possible value of `3a+b` is 2

C

(c) minimum possible value of `6a+b` is `-1`

D

(d) minimum possible value of `6a+b` is 1

Text Solution

Verified by Experts

The correct Answer is:
A, C
Here `Dle0`
and `f(x)ge0,AA x epsilonR`
`:.(f)ge0`
`implies9a+3b+6ge0`
or `3a+bge-2`
`implies`Minimum value of `3a+b` is `-2`.
and `f(6)ge0`
`implies36a+6b+6ge0`
`implies6a=bge-1`
`implies` Minimum value of `6a+b` is `-1`.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise SCQ_TYPE|1 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise The Straight Lines Exercise 8 : (Questions Asked in Previous 13 years Exams)|1 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Three Dimensional Coordinate System Exercise 12 : Question Asked in Previous Years Exam|2 Videos

Similar Questions

Explore conceptually related problems

If ax^(2)-bx+5=0 does not have two distinct real roots, then find the minimun value of 5a+b.

ax^2 + bx + c = 0(a > 0), has two roots alpha and beta such alpha 2, then

Find the value of a if x^3-3x+a=0 has three distinct real roots.

Find the value of a if x^3-3x+a=0 has three distinct real roots.

a, b, c in R, a!= 0 and the quadratic equation ax^2+bx+c=0 has no real roots, then

If f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c is

The real number k for which the equations 2x^3 +3x+k=0 has two distinct real roots in [0,1]

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

Statement -1 If the equation (4p-3)x^(2)+(4q-3)x+r=0 is satisfied by x=a,x=b nad x=c (where a,b,c are distinct) then p=q=3/4 and r=0 Statement -2 If the quadratic equation ax^(2)+bx+c=0 has three distinct roots, then a, b and c are must be zero.

Let alpha and beta be real numbers and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct non-real roots with Re(z)=1, then it is necessary that