Question

Replace * with a number in such a way that the trinomial could be written in the form a(x+b)^2 or a(x-b)^2.

a) 1.5x^2+6x+*

b) 2x^2-5x+*

Answer 1

Solution given;

a. 1.5x^2+6x+*

1.5(x²+4x+*)

1.5(x²+2.2x+2²)

1.5(x+2)²

b) 2x^2-5x+*

2(x²-5x/2+*)

2(x²-2×5/4 ×x +(5/4)²)

2(x-5/4)²

Answer 2

• a) 6
• b) 3.125 or 25/8

Explanation:

a)

• 1.5x² + 6x + * =
• 1.5(x² + 4x + *) =
• 1.5(x² + 2*2x + 4) =
• 1.5(x + 2)²
• * = 1.5*2² = 6

b)

• 2x² - 5x + * =
• 2(x² - 2.5x + *) =
• 2(x² - 2*1.25x + 1.25²)=
• 2(x - 1.25)²
• * = 2*(1.25)² = 3.125 or 25/8