The product of all real roots of the equation x 2- x -6-0 isA- -9B- 6C- 9D- 36

The correct option is A 9 Given equation x^2 |x| 6=0 If x gt; 0, ∴ equation is x^2 x 6=0 ⇒ (x 3)(x+2)=0 ⇒ x=3, x= 2 ⇒ x=3 If x lt; 0, ∴ equation is x^2+ ...

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Byju's Answer

Standard XII

Mathematics

Higher Order Equations

The product o...

Question

The product of all real roots of the equation $x^{2} - | x | - 6 = 0$ is

-9

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Solution

The correct option is A
-9

Given equation $x^{2} - | x | - 6 = 0$
If x > 0,
$∴ e q u a t i o n i s x^{2} - x - 6 = 0$

$\Rightarrow (x - 3) (x + 2) = 0 \Rightarrow x = 3, x = - 2 \Rightarrow x = 3$

If x < 0, $∴ e q u a t i o n i s x^{2} + x - 6 = 0$

$\Rightarrow (x + 3) (x - 2) = 0 \Rightarrow x = - 3, x = 2 \Rightarrow x = - 3$

Hence product of all possible real roots = –9

Suggest Corrections

The product of all real roots of the equation x2−|x|−6=0 is

The correct option is A -9 Given equation x2−|x|−6=0 If x > 0, ∴ equation is x2−x−6=0 ⇒(x−3)(x+2)=0⇒x=3,x=−2⇒x=3 If x < 0, ∴ equation is x2+x−6=0 ⇒(x+3)(x−2)=0⇒x=−3,x=2⇒x=−3 Hence product of all possible real roots = –9

The product of all real roots of the equation $x^{2} - | x | - 6 = 0$ is