1. Complete the following activity to solve the equation 2x² + 13x + 15 = 0 by using the Quadratic Formula.

Activity:

2x² + 13x + 15 = 0
∴ a =   , b = 13, c = 15
Now, b² − 4ac
= 13² − 4 × 2 ×   
= 169 − 120
∴ b² − 4ac = 49

Now, x = $\frac{-b\pm \; <!--\; plus-minus\; sign\; -->\sqrt{b^2-4ac}}{2a}$

∴ x = $\frac{-b\pm \; <!--\; plus-minus\; sign\; -->\sqrt{b^2-4ac}}{2a}$

∴ x = $\frac{-\mathrm{(\; ...\; )}\pm \; <!--\; plus-minus\; sign\; -->\sqrt{49}}{4}$

∴ x = $\frac{-13\pm \; <!--\; plus-minus\; sign\; -->\mathrm{(...)}}{4}$

∴ $x=\frac{-6}{4}$ or $x=\frac{-20}{4}$

∴ x =   or x =  

2. Complete the following activity:
The sum of the squares of two consecutive even natural numbers is 244. Find those numbers.

Activity:

Let, the smaller number be x.

∴ The greater number will be   .

From the given condition,

 x² + (x + 2)² = 244

∴ x² + x² + 4x + 4 −    = 0

∴ 2x² + 4x − 240 = 0

∴ x² + 2x − 120 = 0

∴ x² +    −    − 120 = 0

∴ x(x + 12) −    (x + 12) = 0

∴ (x + 12) (x − 10) = 0

∴ x =    OR x = 10

But, x is a natural number.

∴ It cannot be negative.

∴ x = − 12 is not possible.

∴ x = 10.

∴ The smaller even natural number is 10.

∴ The greater even natural number = x + 2 = 10 + 2 = 12

∴ Those numbers are 10 and 12.