Suppose `a ,b ,c` are the roots of the cubic `x^3-x^2-2=0.` Then the value of `a^3+b^3+c^3` is _____.

If a, b and c are roots of the equation x^3+qx^2+rx +s=0 then the value of r is

If a, b and c be the roots of 3 x^(3)+8 x+7=0 , then the value of (a+b)^(3)+(b+c)^(3)+(c+a)^(3) is equal to

If the equation whose roots are the squares of the roots of the cubic x^3-a x^2+b x-1=0 is identical with the given cubic equation, then (a) a=0,b=3 b. a=b=0 c. a=b=3 d. a ,b , are roots of x^2+x+2=0

If cos A, cosB and cosC are the roots of the cubic x^3 + ax^2 + bx + c = 0 where A, B, C are the anglesof a triangle then find the value of a^2 – 2b– 2c .

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

Let a ,b ,c be real numbers with a!=0a n dl e talpha,beta be the roots of the equation a x^2+b x+c=0. Express the roots of a^3x^2+a b c x+c^3=0 in terms of alpha,betadot

Let a, b, c be real numbers with a = 0 and let alpha,beta be the roots of the equation ax^2 + bx + C = 0 . Express the roots of a^3x^2 + abcx + c^3 = 0 in terms of alpha,beta

If the point A(2,0),B (-6,0), C(3,a-3) lie on the x-axis then the value of a is ______.

In a triangle ABC, if the sides a,b,c, are roots of x^3-11 x^2+38 x-40=0, then find the value of (cosA)/a+(cosB)/b+(cosC)/c

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 __________.