New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Quadratic Equation and Inequalities question

2023 · 13 Apr · Shift 2 · Q28

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

PYQ Library
JEE Main
Mathematics
Quadratic Equation and Inequalities
2023 · 13 Apr · Shift 2 · Q28

Quadratic Equation and Inequalities question

2023 · 13 Apr · Shift 2 · Q28

JEE MainMathematicsQuadratic Equation and InequalitiesMCQ+4 / −1

Let

\alpha, \beta

be the roots of the equation

x^{2}-\sqrt{2} x+2=0

. Then

\alpha^{14}+\beta^{14}

is equal to

A
$-64$
B
$-64 \sqrt{2}$
C
$-128 \sqrt{2}$
D
$-128$

More from Quadratic Equation and Inequalities

Let $[α]$ denote the greatest integer $\leq α$ . Then $[1] + [2] + [3] + \dots + [120]$ is equal to 2023 · Numerical
The number of real roots of the equation $x ∣ x ∣ - 5∣ x + 2∣ + 6 = 0$ , is :2023 · MCQ
The equation $x^{2} - 4 x + [x] + 3 = x [x]$ , where $[x]$ denotes the greatest integer function, has :2023 · MCQ
Let $λ \in R$ and let the equation E be $∣ x ∣^{2} - 2∣ x ∣ + ∣ λ - 3∣ = 0$ . Then the largest element in the set S = { $x + λ : x$ is an integer solution of E} is 2023 · Numerical
The number of real solutions of the equation $3 (x^{2} + \frac{1}{x ^{2}}) - 2 (x + \frac{1}{x}) + 5 = 0$ , is2023 · MCQ
Let $α \in R$ and let $α, β$ be the roots of the equation $x^{2} + 6 0^{\frac{1}{4}} x + a = 0$ . If $α^{4} + β^{4} = - 30$ , then the product of all possible values of $a$ is .2023 · Numerical
Let $λ e 0$ be a real number. Let $α, β$ be the roots of the equation $14 x^{2} - 31 x + 3 λ = 0$ and $α, γ$ be the roots of the equation $35 x^{2} - 53 x + 4 λ = 0$ . Then $\frac{3 α}{β}$ and $\frac{4 α}{γ}$ …2023 · MCQ
Let $α_{1}, α_{2}, ...., α_{7}$ be the roots of the equation $x^{7} + 3 x^{5} - 13 x^{3} - 15 x = 0$ and $∣ α_{1} ∣ \geq ∣ α_{2} ∣ \geq ... \geq ∣ α_{7} ∣$ . Then $α_{1} α_{2} - α_{3} α_{4} + α_{5} α_{6}$ is…2023 · Numerical