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

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Question

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

Solution

Correct option is

(1, 2)

The quadratic equation 3x2 + 2(a2 + 1) x + a2 – 3a + 2 = 0 will have two roots of opposite sign if it has real roots and the product of the roots is negative, that is, if

           

 

Both of these conditions are met if

 

Testing

SIMILAR QUESTIONS

Q1

If 8, 2 are the roots of x2 + ax + β = 0 and 3, 3 are the roots of x2 + α xb = 0 then the roots of x2 + ax + b = 0 are

Q2

The number of real roots of 

Q3

The product of real of the equation  

              is

Q4

Sum of the non – real roots of 

 

Q5

If tan A and tan B are the roots of the quadratic equation x2 – px + q = 0, then value of sin2 (A + B) is

Q6

If x Ïµ R, the number of solution of  = 1 is

Q7

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

Q8

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

Q9

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

Q10

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