`x^3+ax^2-bx-4=0` has (A) at least one negative root (C) one positive and one negative root (B) (D) at least one positive root all real roots 2

If x^2-(a-3)x+a =0 has at least one positive root,then

If a,b,c epsilon R and abgt0, a+2b+4c=0 then equation ax^2+bx+c=0 has (A) both roots positive (B) both roots negative (C) one positive and one negative root (D) both roots imginary

Suppose a, b, c are real numbers, and each of the equations x^(2)+2ax+b^(2)=0 and x^(2)+2bx+c^(2)=0 has two distinct real roots. Then the equation x^(2)+2cx+a^(2)=0 has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything

Let a, b be non-zero real numbers. Which of the following statements about the quadratic equation ax^2 + (a + b)x + b =0 is neccesarily true ? (I) It has at least one negative root (II) It has at least one positive root. (III) Both its roots are real.

If a+b+2c=0, c!=0, then equation ax^2+bx+c=0 has (A) at least one root in (0,1) (B) at least one root in (0,2) (C) at least on root in (-1,1) (D) none of these

If a+b+2c=0, c!=0, then equation ax^2+bx+c=0 has (A) at least one root in (0,1) (B) at least one root in (0,2) (C) at least on root in (-1,1) (D) none of these

Find p in R for which x^2-px+p+3=0 has one positive and one negative root.