Question

Hellp with the quadratic equations (A and B please) thank you

Answer 1

A) x^2 - 8x + 15 = 0. 
Here we multiply  15 and the coefficient of x^2 =  15*1 = 15.

So now we think of two numbers whose product is 15 and its sum gives us the middle coefficient term -8.

15 = -3 * -5.

And -3 + -5 = -8.  We replace the -8 with this expression.

x^2 - 8x + 15 = 0.

x^2 -3x - 5x + 15 = 0.      Factorize now.

x (x - 3)  - 5(x - 3) = 0.

(x -3)(x - 5) = 0.

(x-3) = 0 or (x -5) = 0.

x = 0 +3,    x = 0 +5.    x = 3, or 5.


b) x^2 + 11x + 28 = 0.

Following similar steps like above:

28 = 14(2),  28 = 7(4).
But it is only  7 + 4 = 11. Which gives the middle coefficient. So we adopt 7(4).

x^2 + 11x + 28 = 0
x^2 + 4x + 7x + 28 = 0.    Factorize.
x(x + 4) + 7(x + 4) = 0.
(x + 4)(x +7) = 0.
x+4 = 0 or x+7 = 0.
x = 0-4  or x = 0 -7.    x = -4 or -7.
Cheers.