y = 4x-3
Their sum is 4.
x2-10 = 4x+11 x2-4x-10-11 = 0 x2-4x-21 = 0 (x+3)(x-7) = 0 x = -3 and x = 7
x2 - 4x = 8 x2 - 4x + 4 = 8 + 4 (x - 2)2 = 12 x - 2 = +&- sq. root of 12 x = 2 +&- 2(sq. root of 3)
-3
y = x2-4x+4 Since the highest degree term is 2, it must have 2 roots
No real roots. Imaginary roots as this function does not intersect the X axis.
There are 2 roots to the equation x2-4x-32 equals 0; factored it is (x-8)(x+4); therefore the roots are 8 & -4.
x2 + 4x = 0 ⇒ x(x + 4) = 0 ⇒ x = 0 or x = -4
x2-4x+4 = 0 (x-2)(x-2) = 0 x = 2 or x = 2 It has two equal roots.
4
y = 4x-3
Their sum is 4.
x2 - 4x + 4 = 0 (x - 2)(x - 2) = 0 x = 2
x2 - 4x - 9 = 0 ∴ x2 - 4x = 9 ∴ x2 - 4x + 4 = 13 ∴ (x - 2)2 = 13 ∴ x - 2 = ±√13 ∴ x = 2 ± √13
x2+4x+4 = 25 x2+4x+4-25 = 0 x2+4x-21 = 0 (x+7)(x-3) = 0 x = -7 or x = 3
2x = x2 + 4x - 3 x2 + 2x - 3 = 0 (x - 1)(x - 2) = 0