F4 Math一問~~~~~

Suppose 3+√2 is a root of the quadratic equation x^2-6x+c=0
a ) Find the value of c .
b ) Find the other root of the equation in surd form .
a. x2 – 6x + c = 0

Since 3 + √2 is a root

So, sub x = 3 + √2 into the equation,

(3 + √2)2 – 6(3 + √2) + c = 0

(9 + 6√2 + 2) – 18 - 6√2 + c = 0

c = 7

b. The equation is x2 – 6x + 7 = 0

x = {-(-6) +- √[(-6)2 – 4(1)(7)]} / 2(1)

x = [6 +- √(36 - 28)]/2

x = (6 +- 2√2)/2

x = 3 +-√2

So, the other root is 3 - √2.