Question

Please I need help with this

Answer 1

Answer:

See below

Step-by-step explanation:

We use the identity A + B = -b/a    where A and B are the roots and a and b are the coefficients in ax^2 + bx + c = 0.

So we have

A - B = 1   (given)   and

A + B = -b/a

Adding these 2 equations:-

2A = 1 - b/a   = (a - b)/a

A = (a - b) / 2a     (answer)

Now  A - B = 1

B = A - 1  = (a-b)/2a - 1

=  - (a + b) / 2a. (answer)

Now the last part:-

AB =  (a - b)/2a * - (a + b)/2a

= - (a^2 - b^2) / 4a^2

We now use the identity  AB = c/a

so  -(a^2 - b^2) / 4a^2 = c/a

Cross multiply:-

-a(a^2 - b^2) = 4a^2c

-a^3 + ab^2  = 4a^2 c

ab^2 = a^3 + 4a^2c

divide through by a:-

b^2 = a^2 + 4ac

b^2 = a( a + 4c)  which is what we require.