If `p,q` be non zero real numbes and `f(x)!=0, x in [0,2]` also `f(x)gt0` and `int_0^1 f(x).(x^2+px+q)dx=int_1^2 f(x).(x^2+px+q)dx=0` then equation `x^2+px+q=0` has (A) two imginary roots (B) no root in `(0,2)` (C) one root in `(0,1)` and other in `(1,2)` (D) one root in `(-oo,0)` and other in `(2,oo)`

If b > a , then the equation (x-a)(x-b)-1=0 has (a) both roots in (a ,b) (b) both roots in (-oo,a) (c) both roots in (b ,+oo) (d)one root in (-oo,a) and the other in (b ,+oo)

Equation a/(x-1)+b/(x-2)+c/(x-3)=0(a,b,cgt0) has (A) two imaginary roots (B) one real roots in (1,2) and other in (2,3) (C) no real root in [1,4] (D) two real roots in (1,2)

If b gt a , then the equation (x-a)(x-b)-1=0 has (a) Both roots in (a, b) " " (b) Both roots in (-oo, a) (c) Both roots in (b, +oo) " " (d) One root in (-oo, a) and the other in (b, +oo)

If the equation x^(3) +px +q =0 has three real roots then show that 4p^(3)+ 27q^(2) lt 0 .

If f(x)=(|x-1)/(x^2) the f(x) is one-one in (2,oo) b. one-one in (0,1) c. one-one in (-oo,0) d. one-one in (1,2)

Let a , b , c be nonzero real numbers such that int_0^1(1+cos^8x)(a x^2+b x+c)dx =int_0^2(1+cos^8x)(a x^2+b x+c)dx=0 Then show that the equation a x^2+b x+c=0 will have one root between 0 and 1 and other root between 1 and 2.

Let a , b , c be nonzero real numbers such that int_0^1(1+cos^8x)(a x^2+b x+c)dx =int_0^2(1+cos^8x)(a x^2+b x+c)dx=0 Then show that the equation a x^2+b x+c=0 will have one root between 0 and 1 and other root between 1 and 2.

Statement-1: Let a,b,c be non zero real numbers and f(x)=ax^2+bx+c satisfying int_0^1 (1+cos^8x)f(x)dx=int_0^2(1+cos^8x)f(x)dx then the equation f(x)=0 has at least one root in (0,2) .Statement-2: If int_a^b g(x)dx vanishes and g(x) is continuous then the equation g(x)=0 has at least one real root in (a,b) . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

If one root of the equation x^2+px+q=0 is the square of the other then

If x^(2) - px + q = 0 has equal integral roots, then