For what values of m can the expression 2x2 + mxy + 3y2 - 5y - 2 be expressed as the product of two linear factors?
0
49
C.
We have the expression
2x2 + mxy + 3y2 - 5y - 2
Comparing the given expression with
ax2 + 2hxy + by2 + 2gx + 2fy + c,
we get
a = 2, h = , b = 3, c = - 2, g = 0, f = -
The given expression is resolvable into linear factors, if
abc + 2fgh - af2 - bg2 - ch2 = 0
(2) (3) (- 2) + 2(0) - 2 - 0 - (- 2) = 0
Let be the roots of the equation x2 - ax + b = 0 and . Then, An + 1 - aAn + bAn - 1 is equal to
- a
b
0
a - b
If b2 4ac for the equation ax4 + bx2 + c = 0, then all the roots of the equation will be real if:
b > 0, a < 0, c > 0
b < 0, a > 0, c > 0
b > 0, a > 0, c > 0
b > 0, a > 0, c < 0