Respuesta :
Answer: The correct answers are [tex]x^2-9\text{ and }x^2-100[/tex]
Explanation:
To find the polynomials which could represent the are of a square having side x greater than 2, we need to find the value of 'x' for all the given polynomials.
From the given options:
- 1. [tex]x^2-9[/tex]
[tex]x^2=9\\x=\sqrt{9}\\x=3,-3[/tex]
x = -3 is ignored.
- 2. [tex]x^2-100[/tex]
[tex]x^2=100\\x=\sqrt{100}\\x=\pm10\\x=10,-10[/tex]
x = -10 is ignored
- 3. [tex]x^2-4x+4[/tex]
To solve this we use the quadratic formula:
[tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Putting values of a, b and c, we get:
[tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(4)}}{2\times 1}\\x=2,2[/tex]
As, x comes out to be 2 and is not greater than 2. Hence, this is not considered.
- 4. [tex]x^2+10x+25[/tex]
Solving for 'x' by splitting the middle term:
[tex]\Rightarrow x^2+5x+5x+25\\\Rightarrow x(x+5)+5(x+5)\\x=-5,-5[/tex]
Hence, this is ignored.
- 5. [tex]x^2+15x+36[/tex]
Solving for 'x' by splitting the middle term:
[tex]\Rightarrow x^2+12x+3x+36\\\Rightarrow x(x+12)+3(x+12)\\x=-12,-3[/tex]
Hence, this is ignored.
So, the correct polynomials are [tex]x^2-9\text{ and }x^2-100[/tex]
