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 a x^2+b x+c=0a n db x^2+c x+a=0 have a common root and a, b, and c are nonzero real numbers, then find the value of (a^3+b^3+c^3)//a b c

The equations x^2 +3x+5=0 and ax^2+bx+c=0 have a common root. If a,b,c in N then the least possible values of a+b+c is equal to

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 x^2-10ax-11b =0 have roots c and d. x^2-10cx -11d=0 have roots a and b, then find a+b+c+d.

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .

If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2

If x=1a n dx=2 are solutions of equations x^3+a x^2+b x+c=0a n da+b=1, then find the value of bdot

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+a x+bc=0 a n d x^2+b x+c a=0(a!=b) have a common root, then prove that their other roots satisfy the equation x^2+c x+a b=0.

Let a , b and be the roots of the equation x^2-10 xc -11d =0 and those roots of c and d of x^2-10 a x-11 b=0 ,dot then find the value of a+b+c+d