Question

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

Solution

Correct option is

– 2

Treat as a quadratic in y

 y2 + y (2x + m) + (2x – 3) = 0

 Δ = (2x + m)2 – 4 (2x – 3)

    = 4x2 + 4xm – 8x + m2 + 12 

    = 4x2 + 4x(m – 2) + (m2 + 12) 

    = [4x2 + 4x (m – 2) + (m – 2)2] + (m2 + 12) – (m – 2)2

    = [2x + (m – 2)]2 + [12 + 4m – 4]

For rational factors Δ should be a perfect square

 ∴ 8 + 4 m = 0    or   m = – 2.

SIMILAR QUESTIONS

Q1

If x2 – 4x + log1/2 a does not have two distinct roots, then the maximum value of a

Q2

If the roots of the equation bx2 + cx + a = 0 be expression, then for all real values of x, the expression 3b2 x2 + 6bcx + 2c2 is

Q3

If , for all x Ïµ R, then

Q4

If x is real, the maximum value of  is:

Q5

If the roots the equation ax2 + bx + c = are real and of opposite sign then the roots of the equation α (x – β)2 + β (x – α)2 = 0 are

Q6

abc are length of sides of an scalene triangle. If equation

           

has real and distinct roots, then the value of λ is given by:

Q7

A quadratic equation with rational coefficients can have

Q8

If the roots of ax2 + bx + c = 0 are in the ratio mn then

Q9

For real x, the expression [(x + m)2 – 4mn]/[2(x – n)] can be have any value except

Q10

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