For the equation - x -2- x -6-0- the sum of the real roots isA- 2B- none of theseC- 0D- 1

The correct option is C 0 Let p = |x| ⇒ p^2+p 6=0 ⇒ p^2+3p 2p 6=0 ⇒ (p+3)(p 2)=0 ⇒ p = 3,2 Also,|x| = p ⇒ |x| = 2, or |x|= 3 Modulus can not be negative, ∴ ...

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Standard XIII

Mathematics

Roots of a Quadratic Equation

For the equat...

Question

For the equation $| x |^{2} + | x | - 6 = 0, the sum of the real roots is$

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none of these

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Solution

The correct option is B
0

$L e t p = | x | \Rightarrow p^{2} + p - 6 = 0 \Rightarrow p^{2} + 3 p - 2 p - 6 = 0 \Rightarrow (p + 3) (p - 2) = 0 \Rightarrow p = - 3, 2 A l s o, | x | = p \Rightarrow | x | = 2, o r | x | = - 3 Modulus can not be negative, ∴ | x | = 2 \Rightarrow x = \pm 2 \Rightarrow x = 2 o r - 2 Sum of the roots of x is 0.$

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For the equation |x|2+|x|−6=0,the sum of the real roots is

The correct option is B 0 Let p = |x|⇒ p2+p−6=0⇒p2+3p−2p−6=0⇒(p+3)(p−2)=0⇒p=−3,2Also,|x|=p⇒|x|=2, or |x|=−3Modulus can not be negative,∴|x|=2⇒x=±2⇒x=2 or −2Sum of the roots of x is 0.

For the equation $| x |^{2} + | x | - 6 = 0, the sum of the real roots is$