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

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

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## Question

### 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

#### 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

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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