Question

If (x-2) and (2x-1) are the factors of ax^2 + 5X + b. Show that a-b=0

Answer 1

FIRST

[X-2] = 0         AND     [2X-1] = 0

X = 2                            2X=1 ==> X = 1/2

SO,

P[2] = A[2]²+5[2] + B

P[2] = 4A + 10 + B

==> 4A+B = -10 ..................[1]

P[1/2] = A[1/2]²+5[1/2]

A/4 + 2.5 + B = 0

A+4B/4 = -2.5

A+4B = -10.0......................[2]

EQ [2] FROM [1]

4A+B = -10

A +4B = -10

MULTIPLY eq[2] by  4

4A+B = -10

4A+16B = -10

==> 16B = 0

==> B = 0