Question
The following are quadratic equations in x?
$\text{x}^2-\frac{1}{\text{x}^2}=5$
$\text{x}^2-\frac{1}{\text{x}^2}=5$
✓
Answer
$\text{x}^2-\frac{1}{\text{x}^2}=5$
$\Rightarrow x^4- 1 = 5x^2$
$\Rightarrow x^4 - 5x^2 - 1 = 0$
And $(x^4 - 5x^2 - 1)$ Being a polynomial of degree $4$
$\therefore\ \text{x}^2-\frac{1}{\text{x}^2}=5$ is not a quadratic equation.
$\Rightarrow x^4- 1 = 5x^2$
$\Rightarrow x^4 - 5x^2 - 1 = 0$
And $(x^4 - 5x^2 - 1)$ Being a polynomial of degree $4$
$\therefore\ \text{x}^2-\frac{1}{\text{x}^2}=5$ is not a quadratic equation.
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A card is drawn at random from a pack of well-shuffled 52 playing cards. Complete the following activity to find the probability that the card drawn is
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(ii) Event B: The card drawn is a spade.
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→(i) an ace(Event A)(ii) a spade (Event B).
S is the sample space.
$\therefore n(S)=52$
(i) Event A: The card drawn is an ace.
$\therefore n(A)$ = ⬜
$P(A)$ = ⬜$\quad$$\quad$...(Formula)
$\therefore P(A)=\frac{⬜}{52}$$\quad$$\quad$$\therefore P(A)=\frac{⬜}{13}$
(ii) Event B: The card drawn is a spade.
$\therefore n(B)$ = ⬜
$P(B)=\frac{n(B)}{n(S)}$
$\therefore P(B)=\frac{⬜}{4}$