Let A- x - -x2-x-2-0 and B- - - where - are real roots of the quadratic equation x2-x-2-0 - If a-b- A- B- then the quadratic equation whose roots are a-b is

X^2 |x| 2=0 ⇒ |x|^2 |x| 2 =0 ⇒ (|x| 2) (|x| +1) =0 ⇒ |x| =2 ∴ A={2, 2} x^2+|x| 2=0 ⇒ (|x| 1)(|x|+2)=0 ⇒ x=±1 ∴ B={ 1,0} Hence, A× B= {(2, 1),(2,0),( 2, 1),( ...

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Byju's Answer

Standard XI

Mathematics

Roots of a Quadratic Equation

Let A= x ∈ℝ :...

Question

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 $x^{2} + | x | - 2 = 0 .$ If $(a, b) \in A \times B,$ then the quadratic equation whose roots are $a, b$ is

x^{2} - 2 x = 0

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x^{2} - x - 2 = 0

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x^{2} + 2 x = 0

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x^{2} + 3 x + 2 = 0

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Solution

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

$x^{2} + | x | - 2 = 0$
$\Rightarrow (| x | - 1) (| x | + 2) = 0$
$\Rightarrow x = \pm 1$
$∴ B = {- 1, 0}$
Hence, $A \times B = {(2, - 1), (2, 0), (- 2, - 1), (- 2, 0)}$

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Similar questions

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

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α, β

are the roots of quadratic equation

a x^{2} + b x + c = 0

, then

{(a α + b)}^{- 2} + {(a β + b)}^{- 2} =

Q. If

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x^{3} + 125 = 0

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{(\frac{α}{β})}^{2}

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{(\frac{α}{γ})}^{2}

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and

{(\frac{β}{α})}^{2}

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x^{3} + 27 = 0

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α, β, γ and δ

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Let A={x∈R:x2−|x|−2=0} and B={α+β, αβ} where α,β are real roots of the quadratic equation x2+|x|−2=0. If (a,b)∈A×B, then the quadratic equation whose roots are a,b is

The correct option is D x2+3x+2=0x2−|x|−2=0 ⇒|x|2−|x|−2=0 ⇒(|x|−2)(|x|+1)=0 ⇒|x|=2 ∴A={2,−2} x2+|x|−2=0 ⇒(|x|−1)(|x|+2)=0 ⇒x=±1 ∴B={−1,0} Hence, A×B={(2,−1),(2,0),(−2,−1),(−2,0)}

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 $x^{2} + | x | - 2 = 0 .$ If $(a, b) \in A \times B,$ then the quadratic equation whose roots are $a, b$ is