Number of rational roots of the equation $| x^{2} - 2 x - 3 | + 4 x = 0$ is

1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $1$
$| x^{2} - 2 x - 3 | + 4 x = 0$
$| (x + 1) (x - 3) | + 4 x = 0$
For $x ϵ (- \infty, - 1] \cup [3, \infty)$
$x^{2} - 2 x - 3 + 4 x = 0$
$x^{2} + 2 x - 3 = 0$
$(x + 3) (x - 1) = 0$
$x = - 3$ and $x = 1$
However $x = 1$ does not fall in the above range.
Hence $x = - 3$ is a possible real root.
For $x ϵ (- 1, 3)$
$- x^{2} + 2 x + 3 + 4 x = 0$
$- x^{2} + 6 x + 3 = 0$
$x^{2} - 6 x - 3 = 0$
$(x - 3)^{2} - 12 = 0$
$(x - 3)^{2} = 12$
$(x - 3) = \pm 2 \sqrt{3}$
$x = 3 \pm 2 \sqrt{3}$ ... irrational roots.
Hence there exists only one rational root that is $x = - 3$

Suggest Corrections

Similar questions

Q. Rational roots of the equation

2 x^{4} + x^{3} - 11 x^{2} + x + 2 = 0

are

Q. The number of real roots of the equation

2 x^{4} - 4 x^{3} - 4 x + 2 = 0

Q. If

α, β

are the root of a quadratic equation

x^{2} - 3 x + 5 = 0

, then the equation whose roots are

(α^{2} - 3 α + 7) and (β^{2} - 3 β + 7)

Q. Find the number of rational roots of the equation

2 x^{99} + 3 x^{98} + 2 x^{97} + . . . + 2 x + 3 = 0

Question 10
Which of the following equations has no real roots?
(A) $x^{2} - 4 x + 3 \sqrt{2} = 0$
(B) $x^{2} + 4 x - 3 \sqrt{2} = 0$
(C) $x^{2} - 4 x - 3 \sqrt{2} = 0$
(D) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$

Join BYJU'S Learning Program

Number of rational roots of the equation |x2−2x−3|+4x=0 is

Number of rational roots of the equation $| x^{2} - 2 x - 3 | + 4 x = 0$ is