Let `x^2-3x+p=0` has two positive roots `aa n db` , then minimum value if `(4/a+1/b)` is,

If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum value of (a^(2)+1)//(a^(2)+2) is

If the cubic 2x^3-9x^2+12 x+k=0 has two equal roots then minimum value of |k| is______.

If the cubic 2x^3-9x^2+12 x+k=0 has two equal roots then minimum value of |k| is______.

If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+c

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

If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a common positive root, then find the values of aa n dbdot

If the roots of ht cubic, x^3+a x^2+b x+c=0 are three consecutive positive integers, then the value of (a^2//b+1) is equal to __________.

Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alphaa n dbeta,w h e r ealpha >1 , then show that 1+c/a+|b/a|<0

If alpha,a n dbeta be t roots of the equation x^2+p x-1//2p^2=0,w h e r ep in Rdot Then the minimum value of alpha^4+beta^4 is 2sqrt(2) b. 2-sqrt(2) c. 2 d. 2+sqrt(2)

The function k f(x)=a x^3+b x^2+c x+d has three positive roots. If the sum of the roots of f(x) is 4, the larget possible inegal values of c//a is ____________.