Question

Question 2 Find the missing number that makes the expression a perfect square. a. x2 3 + 16 b. x2 + 2 – 25

Answer 1

Finding the missing number that makes the expression a perfect square.

a) x ^2 - p x + 16, where p is the missing number

comparing with a x^2 + bx + c = 0 ( General Quadratic Equation)

a = 1 , b = -p , c = 16

Using b ^2 = 4ac , we have:

( -p ) ^2 = 4 x 1 x 16

p ^ 2 = 64

square root both sides, we have :

p = 8

b) Finding the missing number that makes the expression a perfect square.

x ^2 + p x - 25 , where p is the missing number

comparing with a x^2 + bx + c = 0 ( General Quadratic Equation)

a = 1 , b = p , c = - 25

Using b ^2 = 4ac , we have:

( p ) ^2 = 4 x 1 x -25

p ^2 = - 100

square root both sides, we have:

p = 10 i ( where i is an imaginary number )