**I/GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Short Questions**

**Exam Questions:**

1) Find the values (s) of k so that the quadratic equation 3x^{2} − 2kx + 12 = 0 has equal roots.

2) The sum of first 20 odd natural number is..?

**Answers:**

For I/GCSE Mathematics, you should know:

1) First, let's compare the given quadratic equation with the general quadratic equation of ax^{2} + bx + c = 0.

**In doing so, we obtain the following values:a = 3, b = -2k, c = 12.**

The discriminant (D) of the given quadratic equation would be:

D = b^{2} - 4ac

= (-2k)^{2 }- 4 x 3 x 12

= **4k**^{2}** - 144**.

For **equal roots**, the discriminant should **equal to 0**.

D = 0

4k^{2} - 144 = 0

4(k^{2} - 36) = 0

k^{2} = 36**k = +-6**.

As such, the values of the given quadratic equation will have equal roots **6 and -6**.

2) In the first 20 odd natural numbers:

The first term, **a**, is **equal to 1**.

The common difference, **d**, is **equal to 2**.

So, the sum of the first n terms is **n/2[2a + (n - 1)d]**

From this, we find that **n = 20**, **a = 1** and **d = 2**.

Substituting these in, we get the sum of the first 20 natuarl numbers: 20/2[2(1) + (20 - 1)2]

= 10 x (2 + 19 x 2) = 10 x 40 = **400**.

Work hard for your I/GCSE Mathematics examination!

End of analysis. Great!