Find an equation with integral co-efficients, whose roots are the squares of the roots of the equation 2×2 + 5x – 6 = 0

a) i) Find the minimum value of x2 – 5x – 7 and state the value of x
when the minimum value occurs. (3 marks)

ii) Rationarise the denominator of (2 marks)

b) i) If are the roots of the equation 2×2 – 5x – 1 = 0, find the value of . (2 marks)

ii) The expression ax4 + bx3 – x2 + 2x + 3 has remainder 3x + 5 when
it is divided by x2 – x – 2. Find the values of a and b. (3 marks)

c) Find the sum of odd numbers between 11 and 199 inclusive. (4 marks)

d) Given that sin Find the value of (i) sin 2 (3 marks)
e) Eliminate from the equations x = 2 tan and y = tan 2 . (3 marks)

f) i) Find the probability of getting three heads in five tosses of unfair
coin in which the probability of getting a head is (3 marks)

ii) Find the mean and standard deviation of the numbers 2, 3, 4, 5, 6 and 7(3 marks)

g) How many arrangements can be made of the letters in the word
TROTTING? In how many of these are N and G next to each other? (3 marks)



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