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

Find p in R for which x^2-px+p+3=0 has one root>2 and the other root<2.

If alpha and beta are the roots of x^(2)+px+q=0and alpha^(4),beta^(4) are the roots of x^(2)-rx+s=0, then the equation x^(2)-4qx+2q^(2)-r=0 has always.A.one positive and one negative root B.two positive roots C.two negative root B.cannot say anything

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

If a,b,c in R and abc<0, then equation bcx^(2)+(2b+c-a)x+a=0 has (a).both positive roots (b) both negative roots (c).real roots (d) one positive and one negative root

If positive numbers a,b,c are in H.P.then equation x^(2)-kx+2b^(101)-a^(101)-c^(101)=0(k in R) has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

The quadratic equation x^(2)-(p-4)x+p^(2)=0 has (1) Real and distinct roots if pe-4,(2) Both roots positive if pe (3) Both roots negative if pel-4,(4) One root positive and one negative root for 13. pe ?

If p and q are distinct primes and x^(2)-px+q=0 has distinct positive integral roots p+q=?

If both roots of x^(2)+px+q=0 are positive and one root is cube of other root,then -

Statement-1: If a, b, c in R and 2a + 3b + 6c = 0 , then the equation ax^(2) + bx + c = 0 has at least one real root in (0, 1). Statement-2: If f(x) is a polynomial which assumes both positive and negative values, then it has at least one real root.

The set of values of p for which x^(2)-2px+3p+4 is negative for atleast one real x is