Answer:

Step-by-step explanation:
If α + β are the roots of the equation ax² + bx + c = 0 then
(x - α)(x - β) = 0, that is
x² - x(α + β) + αβ = 0
comparing the equation with ax² + bx + c = 0 ( ie. x² +
+
= 0 ) then
α + β = -
, αβ = 
comparing 3x² - 12x + 7 = 0 with ax² + bx + c = 0, gives
a = 3, b = - 12, c = 7, hence
α + β = -
= 4 and αβ = 
(α + β)² = α² + β² + 2αβ
α² + β² = (α + β)² - 2αβ = 4² -
= 
Answer:
36x + 45
Step-by-step explanation:
given
9(3x + 5 + x) ← collect like terms inside parenthesis
= 9(4x + 5)
Multiply the terms inside the parenthesis by the 9 outside
= (9 × 4x) + (9 × 5)
= 36x + 45
A)
a³ * a⁵ = a⁵⁺³
= a⁸
b)
b⁶ / b³ = b⁶⁻³
= b³
c)
4c⁷ * 3c⁵ = (4 * 3)c⁷⁺⁵
= 12c¹²
d)
12p⁶ / 4p² = (12 / 4)p⁶⁻²
= 3p⁴
e)
(3p²q³)³ = (3)³(p²)³(q³)³
= 27p²⁽³⁾q³⁽³⁾
= 27p⁶q⁹
f)
Shaded area = Area of large rectangle - Area of smaller rectangle
Area of large rectangle = 5(4x - 2)
= 20x - 10
Area of smaller rectangle = 3(2x - 3)
= 6x - 9
Shaded area = (20x - 10) - (6x - 9)
= 20x - 6x - 10 + 9
= 14x - 1