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Number of Elements in a Cartesian Product

Let A = x : x...

Question

Let $A = {x : x is a root of the equation x^{3} + 2 x^{2} - x - 2 = 0}$ and $B = {x : x is a prime divisor of 720},$ then $n (A \times B)$ is

6

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Solution

The correct option is B $9$
$x^{3} + 2 x^{2} - x - 2 = 0 \Rightarrow (x^{2} - 1) (x + 2) = 0 \Rightarrow (x - 1) (x + 1) (x + 2) = 0 ∴ x = 1, - 1, - 2 \Rightarrow A = {- 1, 1, - 2}$

Prime divisors of $720$ are $2, 3, 5.$
$\Rightarrow B = {2, 3, 5} ∴ n (A \times B) = n (A) \times n (B) = 9$

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Similar questions

Q. Let

A = {x : x is a root of the equation x^{3} + 2 x^{2} - x - 2 = 0}

and

B = {x : x is a prime divisor of 720},

then

n (A \times B)

Q. If

a

and

b

are the roots of equation

x^{2} + px + 1 = 0 and c,

d are the roots of equation

x^{2} + qx + 1 = 0

, then the value of

E = (a - c) (b - c) (a + d) (b + d)

Suppose $a, b ϵ R a n d a \neq 0, b \neq 0$ . Let $α, β$ be the roots of $x^{2} + a x + b = 0$ . Find the equation whose roots are $α^{2}$ , $β^{2}$ .

Q. Let

A = {x \in R : x^{2} - | x | - 2 = 0}

and

B = {α + β, α β}

where

α, β

are real roots of the quadratic equation

x^{2} + | x | - 2 = 0 .

(a, b) \in A \times B,

then the quadratic equation whose roots are

a, b

Q. If the roots of the equation

(x - a) (x - b) + (x - b) (x - c) + (x - c) (x - a) = 0

are equal, then

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is equal to

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Let A={x:x is a root of the equation x3+2x2−x−2=0} and B={x:x is a prime divisor of 720 }, then n(A×B) is

The correct option is B 9x3+2x2−x−2=0⇒(x2−1)(x+2)=0⇒(x−1)(x+1)(x+2)=0∴x=1,−1,−2⇒A={−1,1,−2} Prime divisors of 720 are 2,3,5. ⇒B={2,3,5}∴n(A×B)=n(A)×n(B)=9

Let $A = {x : x is a root of the equation x^{3} + 2 x^{2} - x - 2 = 0}$ and $B = {x : x is a prime divisor of 720},$ then $n (A \times B)$ is

The correct option is B $9$
$x^{3} + 2 x^{2} - x - 2 = 0 \Rightarrow (x^{2} - 1) (x + 2) = 0 \Rightarrow (x - 1) (x + 1) (x + 2) = 0 ∴ x = 1, - 1, - 2 \Rightarrow A = {- 1, 1, - 2}$

Prime divisors of $720$ are $2, 3, 5.$
$\Rightarrow B = {2, 3, 5} ∴ n (A \times B) = n (A) \times n (B) = 9$