I/GCSE Mathematics Question Analysis Topic: Mathematics - Short Questions
Exam Questions:
1) Find the values (s) of k so that the quadratic equation 3x2 − 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 ax2 + 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 = b2 - 4ac
= (-2k)2 - 4 x 3 x 12
= 4k2 - 144.
For equal roots, the discriminant should equal to 0.
D = 0
4k2 - 144 = 0
4(k2 - 36) = 0
k2 = 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!