Question

SECTION A: Compulsory QUESTION 1 Consider the subsets \( A=[1,4], B=(2,8) \) and \( C=[3,6) \) of the universal set \( (0,10] \). Find each of the following sets and display them on the number line. i) \( (A \cap B) \) ii) C' iii) \( B^{\prime} \cap A \) iv) \( (A \cup B)^{\prime} \) [10 Marks] b) The quadratic equation \( 2 x^{2}-4 x+5=0 \) roots \( \alpha \) and \( \beta \). Find the value of: i) \( (\alpha-\beta)^{2} \) [4 Marks] ii) \( \frac{1}{\alpha}+\frac{1}{\beta} \) [4 Marks] c) By using the Synthetic method. Find the Quotient \& Remainder when the polynomial \( P(x)=x^{3}+125 \) is divided by \( (x-5) \). [7 Marks]

          SECTION A: Compulsory
QUESTION 1
Consider the subsets \( A=[1,4], B=(2,8) \) and \( C=[3,6) \) of the universal set \( (0,10] \). Find each of the following sets and display them on the number line.
i) \( (A \cap B) \)
ii) C'
iii) \( B^{\prime} \cap A \)
iv) \( (A \cup B)^{\prime} \)
[10 Marks]
b) The quadratic equation \( 2 x^{2}-4 x+5=0 \) roots \( \alpha \) and \( \beta \). Find the value of:
i) \( (\alpha-\beta)^{2} \)
[4 Marks]
ii) \( \frac{1}{\alpha}+\frac{1}{\beta} \)
[4 Marks]
c) By using the Synthetic method. Find the Quotient \& Remainder when the polynomial \( P(x)=x^{3}+125 \) is divided by \( (x-5) \).
[7 Marks]

SECTION A: Compulsory
QUESTION 1
Consider the subsets A=[1,4], B=(2,8) and C=[3,6) of the universal set (0,10]. Find each of the following sets and display them on the number line.
i) (A ∩ B)
ii) C'
iii) B^'∩ A
iv) (A ∪ B)^'
[10 Marks]
b) The quadratic equation 2 x^2-4 x+5=0 roots α and β. Find the value of:
i) (α-β)^2
[4 Marks]
ii) (1)/(α)+(1)/(β)
[4 Marks]
c) By using the Synthetic method. Find the Quotient & Remainder when the polynomial P(x)=x^3+125 is divided by (x-5).
[7 Marks]

Added by Paul K.

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