If be the roots of the quadratic equation x2 + x + 1 = 0, then the equation whose roots are f is
x2 - x + 1 = 0
x2 - x - 1 = 0
x2 + x - 1 = 0
x2 + x + 1 = 0
The roots of the quadratic equation are
imaginary
real, rational and equal
real, irrational and unequal
real, rational and unequal
The quadratic equation x2 + 15 + 14 = 0 has
only positive solutions
only negative solutions
no solution
both positive and negative solution
If a, b, c are real, then both the roots of the equation (x - b)(x - c) + (x - c)(x - a) + (x - a)(x - b) = 0
positive
negative
real
imaginary
C.
real
Given equation can be rewritten as,
3x2 - 2x(a + b + c) + ab + bc + ca = 0
Now, Discriminant,
D = 4(a + b + c)2 - 4 . 3(ab + bc + ca)
= 4(a2 + b2 + c2 - ab - bc - ca)
= 2[(a - b)2 + (b - c)2 + (c - a)2]
0
Hence, roots are real.
The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 is
ax2 + 3bx + 3c = 0
ax2 + 3bx + c
9ax2 + 9bx + c
ax2 + bx + 3c