Question

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

Solution

Correct option is

Real and unequal

Discriminant of the given equation is

          D = 9 (l – m)2 + 8 (l + m)2

As l + m ≠ 0, (l + m)2 > 0. Also, (l – m)2 ≥ 0.

Thus, D > 0

Hence, roots of the given equation are real and unequal.

SIMILAR QUESTIONS

Q1

If the expression y2 + 2xy + 2x + my – 3 can be resolved into two rational factors, then m must be

Q2

If one root of the equation x2 + px + 12 = 0 is 4, while the equation x2 +px + q = 0 has equal roots, the value of q is

Q3

If x2 + px + 1 is a factor of ax2 + bx + c, then

Q4

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

Q5

The number of real roots of 

Q6

The product of real of the equation  

              is

Q7

Sum of the non – real roots of 

 

Q8

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

Q9

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

Q10

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