If Both The Roots Of The Equation x2 – 6ax + 2 – 2a + 9a2 = 0 Exceed 3, Then

Why Kaysons ?

Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

If both the roots of the equation x2 – 6ax + 2 – 2a + 9a2 = 0 exceed 3, then

Solution

Correct option is

a > 11/9

We can write the given equation

        (x – 3a)2 = 2a – 2

Note that a ≥ 1 and

        

Both the roots will exceed 3 if smaller of the two roots exceed 3, that is, if

           

 

 

 

Testing

SIMILAR QUESTIONS

Q1

If lmn are real, l + m ≠ 0, then the roots of the equation

         (l + m)x2 – 3(l – m)x – 2 (l + m) = 0 are

Q2

The real values of a for which the sum of the squares of the roots of the equation x2 – (a – 2) x – a – 1 = 0 assume the least value is

Q3

If p and q are distinct primes and x2 – px + = 0 has distinct positive roots, then p + equals

Q4

The real values of a for which the quadratic equation 3x2 + 2 (a2 + 1) x+(a2 – 3a + 2) = 0 possesses roots opposite signs lie in

Q5

If abc Ïµ R and a + b + c = 0, then the quadratic equation 3 ax2 + 3ax2 + 2bx + c = 0 has

Q6

Let f (x) = ax2 + bx + cac, Ïµ R and a ≠ 0. Suppose (x) > 0 for all x Ïµ R.

Let g (x) = f (x) + f ’ (x) + f ”(x). Then

Q7

If b < 0, then the roots x1 and x2 of the equation 2x2 + 6x + b = 0, satisfy the condition (x1/x2) < k where k is equal to.

Q8

If ax2 + bx + cabc Ïµ R has no real zeros, and if c < 0, then,

Q9

If x is real, then the maximum value of