if `(x-a)(x-5)+2=0` has only integral roots where `a in I ,` when value of `' a '` can be: `8` b. `7` c. `6` d. `5`

If x^(2)+2bx+9b-14=0 has only negative roots then integral value of 'b' can be

The total number of values a so that x^2-x-a=0 has integral roots, where a in Na n d6lt=alt=100 , is equal to a.2 b. 4 c. 6 d. 8

Consider the equations (x-p)(x-6)+1 = 0 having integral coefficents. If the equation has integral roots, then what values can p have?

If the equation ax^(2)+bx+c=x^(3)+(1)/(x)(a.b.c<=0) has only real roots and all the roots are integers then the value of (-a-b-c)/(7) is

Match the following : {:("Column I" , " Column II"),(" (A) The total number or real solutions of the equation" (x^(2)-7x+1)^((x^(2)-11x+30)) =1 "is", "(p)" 2), ("(B) Total number of values of a so that " x^(2) -x-a=0 " has distinct integral roots, where a" in and 6 ge a ge 100 " is equal to " , "(q)" 4),("(C) The least value of n such that " (n-2)x^(2) + 8x + n +4 gt 0 AA x in R " where " n in N "is" , "(r)" 5 ),("(D) Total number of integral values of a such that " x^(2) +ax +a +1=0 " has integral roots is equal to " , "(t)" 8),(,"(t)"9):}

Show that the equation x^(3)+2x^(2)+x+5=0 has only one real root, such that [alpha]=-3 , where [x] denotes the integral point of x

If the roots of 2x^(2)+7x+5=0 are reciprocals roots of ax^(2)+bx+c=0 then find the value of a-c