New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Quadratic Equation and Inequalities question

2022 · 27 Jun · Shift 1 · Q37

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Quadratic Equation and Inequalities
2022 · 27 Jun · Shift 1 · Q37

Quadratic Equation and Inequalities question

2022 · 27 Jun · Shift 1 · Q37

JEE MainMathematicsQuadratic Equation and InequalitiesNumerical+4 / −1

If the sum of all the roots of the equation

{e^{2x}} - 11{e^x} - 45{e^{ - x}} + {{81} \over 2} = 0

is

{\log _e}p

, then p is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Quadratic Equation and Inequalities

Let $α$ , $β$ be the roots of the equation $x^{2} - 4 λ x + 5 = 0$ and $α$ , $γ$ be the roots of the equation $x^{2} - (32 + 23) x + 7 + 3 λ 3 = 0$ , $λ$ > 0. If $β + γ = 32$ …2022 · Numerical
The sum of all real values of $x$ for which $\frac{3 x ^{2} - 9 x + 17}{x ^{2} + 3 x + 10} = \frac{5 x ^{2} - 7 x + 19}{3 x ^{2} + 5 x + 12}$ is equal to .2022 · Numerical
$Let S = {x \in [- 6, 3] - {- 2, 2} : \frac{∣ x + 3∣ - 1}{∣ x ∣ - 2} \geq 0} and T = {x \in Z : x^{2} - 7∣ x ∣ + 9 \leq 0} .$ Then the number of elements in $S \cap T$ is :2022 · MCQ
Let $α$ , $β$ be the roots of the equation $x^{2} - 2 x + 6 = 0$ and $\frac{1}{α ^{2}} + 1, \frac{1}{β ^{2}} + 1$ be the roots of the equation $x^{2} + a x + b = 0$ . Then the roots of the equation $x^{2} - (a + b - 2) x + (a + b + 2) = 0$ …2022 · MCQ
The number of real solutions of the equation $e^{4 x} + 4 e^{3 x} - 58 e^{2 x} + 4 e^{x} + 1 = 0$ is .2022 · Numerical
Let f(x) be a quadratic polynomial such that f( $-$ 2) + f(3) = 0. If one of the roots of f(x) = 0 is $-$ 1, then the sum of the roots of f(x) = 0 is equal to :2022 · MCQ
If $\frac{1}{( 20 - a ) ( 40 - a )} + \frac{1}{( 40 - a ) ( 60 - a )} + \dots + \frac{1}{( 180 - a ) ( 200 - a )} = \frac{1}{256}$ , then the maximum value of $a$ is :2022 · MCQ
Let $α, β (α > β)$ be the roots of the quadratic equation $x^{2} - x - 4 = 0.$ If $P_{n} = α^{n} - β^{n}$ , $n \in N$ , then $\frac{P _{15} P _{16} - P _{14} P _{16} - P _{15}^{2} + P _{14} P _{15}}{P _{13} P _{14}}$ is equal…2022 · Numerical