New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Quadratic Equation and Inequalities question

2023 · 29 Jan · Shift 1 · Q22

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

PYQ Library
JEE Main
Mathematics
Quadratic Equation and Inequalities
2023 · 29 Jan · Shift 1 · Q22

Quadratic Equation and Inequalities question

2023 · 29 Jan · Shift 1 · Q22

JEE MainMathematicsQuadratic Equation and InequalitiesMCQ+4 / −1

Let

\lambda e 0

be a real number. Let

\alpha,\beta

be the roots of the equation

14{x^2} - 31x + 3\lambda = 0

and

\alpha,\gamma

be the roots of the equation

35{x^2} - 53x + 4\lambda = 0

. Then

{{3\alpha } \over \beta }

and

{{4\alpha } \over \gamma }

are the roots of the equation

A
$7{x^2} - 245x + 250 = 0$
B
$49{x^2} - 245x + 250 = 0$
C
$49{x^2} + 245x + 250 = 0$
D
$7{x^2} + 245x - 250 = 0$

More from Quadratic Equation and Inequalities

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
If the value of real number $a > 0$ for which $x^{2} - 5 a x + 1 = 0$ and $x^{2} - a x - 5 = 0$ have a common real root is $\frac{3}{2 β}$ then $β$ is equal to .2023 · Numerical
The number of real roots of the equation $x^{2} - 4 x + 3 + x^{2} - 9 = 4 x^{2} - 14 x + 6$ , is :2023 · MCQ
The equation $e^{4 x} + 8 e^{3 x} + 13 e^{2 x} - 8 e^{x} + 1 = 0, x \in R$ has :2023 · MCQ
If the sum of the squares of the reciprocals of the roots $α$ and $β$ of the equation 3x2 + $λ$ x $-$ 1 = 0 is 15, then 6( $α$ 3 + $β$ 3)2 is equal to :2022 · MCQ
The sum of all the real roots of the equation $(e^{2 x} - 4) (6 e^{2 x} - 5 e^{x} + 1) = 0$ is2022 · MCQ
The number of distinct real roots of the equation x7 $-$ 7x $-$ 2 = 0 is2022 · MCQ
If $α, β, γ, δ$ are the roots of the equation $x^{4} + x^{3} + x^{2} + x + 1 = 0$ , then $α^{2021} + β^{2021} + γ^{2021} + δ^{2021}$ is equal to :2022 · MCQ