For the equation |x^2| + |x| - 6 = 0,the root | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equation: $|x^2| + |x| - 6 = 0$.Since $|x^2| = |x|^2$,the equation can be written as $|x|^2 + |x| - 6 = 0$.Let $t = |x|$,where $t \ge 0$. Th

Vedclass · Accepted Answer

Real with sum zero

Vedclass · Answer

(C) Given equation: $|x^2| + |x| - 6 = 0$.Since $|x^2| = |x|^2$,the equation can be written as $|x|^2 + |x| - 6 = 0$.Let $t = |x|$,where $t \ge 0$. The equation becomes $t^2 + t - 6 = 0$.Factoring the quadratic: $(t + 3)(t - 2) = 0$.This gives $t = -3$ or $t = 2$.Since $t = |x| \ge 0$,we discard $t = -3$.Thus,$|x| = 2$,which implies $x = 2$ or $x = -2$.The roots are $2$ and $-2$.The sum of the roots is $2 + (-2) = 0$.

For the equation $|x^2| + |x| - 6 = 0$,the roots are

Similar Questions

The roots of the equation $a(b-c)x^2 + b(c-a)x + c(a-b) = 0$ are

The quadratic equation $p(x) = 0$ with real coefficients has purely imaginary roots. Then the equation $p(p(x)) = 0$ has

If the equation $x^2 + \lambda x + \mu = 0$ has equal roots and one root of the equation $x^2 + \lambda x - 12 = 0$ is $2$,then $(\lambda, \mu) = $

Let $f(x) = x^2 + ax + b$,where $a, b \in R$. If $f(x) = 0$ has all its roots imaginary,then the roots of $f(x) + f'(x) + f''(x) = 0$ are

Two positive distinct numbers $a$ and $b$ each differ from their reciprocal by $1$. The value of $a + b$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module