If `l ,m ,n` are real `l!=m` , then the roots of the equation `(l-m)x^2-5(l_+m)x-2(l-m)=0` are a. real and equal b. Complex c. real and unequal d. none of these

If a, b are real then show that the roots of the equation (a-b)x^(2)-6(a+b)x-9(a-b)=0 are real and unequal.

If a

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

Find all the value of m for which the equation sin^2x-(m-3)sinx+m=0 has real roots.

The integral value of m for which the root of the equation m x^2+(2m-1)x+(m-2)=0 are rational are given by the expression [where n is integer] (A) n^2 (B) n(n+2) (C) n(n+1) (D) none of these

The pair of lines whose direction cosines are given by the equations 3l+m+5n=0a n d6m n-2n l+5l m=0 are a. parallel b. perpendicular c. inclined at cos^(-1)(1/6) d. none of these

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-48=0, then the minimum value of (1//l)+(2//m)+(3//n) equals (a) 1 (b) 2 (c) 3//2 (d) 5//2

The number of integral values of m for which the equation (1+m^(2))x^(2)-2(1+3m)x+(1+8m)=0, has no real roots is