Transformation of Equations

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JEE Advanced 1997

LEVELJEE Main

The sum of all the real roots of the equation $∣ x - 2 ∣^{2} + ∣ x - 2∣ - 2 = 0$ is .........

JEE Advanced 1985

LEVELJEE Main

Solve for $x : (5 + 26)^{x^{2} - 3} + (5 - 26)^{x^{2} - 3} = 10$

JEE Main 2020 (9 January Shift 1)

LEVELJEE Main

The number of real roots of the equation, $e^{4 x} + e^{3 x} - 4 e^{2 x} + e^{x} + 1 = 0$ is:

(A)

3

(B)

4

(C)

1

(D)

2

JEE Main 2020 - 9 Jan (Morning)

LEVELJEE Main

Find number of real roots of equation $e^{4 x} + e^{3 x} - 4 e^{2 x} + e^{x} + 1 = 0$ is

JEE Main 2020 - 5 Sep (Morning)

LEVELJEE Main

The product of the roots of the equation $9 x^{2} - 18∣ x ∣ + 5 = 0$ , is:

JEE Main 2021 (27 July Shift 2)

LEVELJEE Main

The number of real roots of the equation $e^{4 x} - e^{3 x} - 4 e^{2 x} - e^{x} + 1 = 0$ is equal to

JEE Main 2022 (26 June Shift 1)

LEVELJEE Main

The sum of the cubes of all the roots of the equation $x^{4} - 3 x^{3} - 2 x^{2} + 3 x + 1 = 0$ is ______.

JEE Main 2023 (31 January Shift 2)

LEVELJEE Main

The equation $e^{4 x} + 8 e^{3 x} + 13 e^{2 x} - 8 e^{x} + 1 = 0, x \in R$ has:

(A)

two solutions and both are negative

(B)

no solution

(C)

four solutions two of which are negative

(D)

two solutions and only one of them is negative

JEE Main 2025 (January)

LEVELBoard

The number of solutions of the equation $(\frac{9}{x} - \frac{9}{x} + 2) (\frac{2}{x} - \frac{7}{x} + 3) = 0$ is:

JEE Main 2026 (23 January Shift 1)

LEVELJEE Main

If $α$ and $β (α < β)$ are the roots of the equation $(- 2 + 3) (∣ x - 3∣) + (x - 6 x) + (9 - 23) = 0, x \geq 0$ , then $\frac{β}{α} + α β$ is equal to :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The sum of all the real roots of the equation ∣x−2∣2+∣x−2∣−2=0 is .........

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Solve for x:(5+26​)x2−3+(5−26​)x2−3=10

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of real roots of the equation, e4x+e3x−4e2x+ex+1=0 is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Find number of real roots of equation e4x+e3x−4e2x+ex+1=0 is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The product of the roots of the equation 9x2−18∣x∣+5=0, is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of real roots of the equation e4x−e3x−4e2x−ex+1=0 is equal to

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The sum of the cubes of all the roots of the equation x4−3x3−2x2+3x+1=0 is ______.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The equation e4x+8e3x+13e2x−8ex+1=0,x∈R has:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The number of solutions of the equation (x9​−x​9​+2)(x2​−x​7​+3)=0 is:

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If α and β(α<β) are the roots of the equation (−2+3​)(∣x​−3∣)+(x−6x​)+(9−23​)=0,x≥0, then αβ​​+αβ​ is equal to :

The sum of all the real roots of the equation $∣ x - 2 ∣^{2} + ∣ x - 2∣ - 2 = 0$ is .........

Solve for $x : (5 + 26)^{x^{2} - 3} + (5 - 26)^{x^{2} - 3} = 10$

The number of real roots of the equation, $e^{4 x} + e^{3 x} - 4 e^{2 x} + e^{x} + 1 = 0$ is:

Find number of real roots of equation $e^{4 x} + e^{3 x} - 4 e^{2 x} + e^{x} + 1 = 0$ is

The product of the roots of the equation $9 x^{2} - 18∣ x ∣ + 5 = 0$ , is:

The number of real roots of the equation $e^{4 x} - e^{3 x} - 4 e^{2 x} - e^{x} + 1 = 0$ is equal to

The sum of the cubes of all the roots of the equation $x^{4} - 3 x^{3} - 2 x^{2} + 3 x + 1 = 0$ is ______.

The equation $e^{4 x} + 8 e^{3 x} + 13 e^{2 x} - 8 e^{x} + 1 = 0, x \in R$ has:

The number of solutions of the equation $(\frac{9}{x} - \frac{9}{x} + 2) (\frac{2}{x} - \frac{7}{x} + 3) = 0$ is:

If $α$ and $β (α < β)$ are the roots of the equation $(- 2 + 3) (∣ x - 3∣) + (x - 6 x) + (9 - 23) = 0, x \geq 0$ , then $\frac{β}{α} + α β$ is equal to :