New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Quadratic Equation and Inequalities question

2008 · Shift 2 · Q40

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

PYQ Library
JEE Advanced
Mathematics
Quadratic Equation and Inequalities
2008 · Shift 2 · Q40

Quadratic Equation and Inequalities question

2008 · Shift 2 · Q40

JEE AdvancedMathematicsQuadratic Equation and InequalitiesMCQ+3 / −1

Let

a,\,b,c

,

p,q

be real numbers. Suppose

\alpha ,\,\beta

are the roots of the equation

{x^2} + 2px + q = 0

and

\alpha ,{1 \over \beta }

are the roots of the equation

a{x^2} + 2bx + c = 0,

where

{\beta ^2} \in \left\{ { - 1,\,0,\,1} \right\}

STATEMENT - 1 :

\left( {{p^2} - q} \right)\left( {{b^2} - ac} \right) \ge 0

and STATEMENT - 2 :

b e pa

or

c e qa

A
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is a correct explanation for STATEMENT - 1
B
STATEMENT - 1 is True, STATEMENT - 2 is True; STATEMENT - 2 is NOT a correct explanation for STATEMENT - 1
C
STATEMENT - 1 is True, STATEMENT - 2 is False
D
STATEMENT - 1 is False, STATEMENT - 2 is True

More from Quadratic Equation and Inequalities

Let $α, β$ be the roots of the equation $x^{2} - p x + r = 0$ and $\frac{α}{2}, 2 β$ be the roots of the equation $x^{2} - q x + r = 0$ . Then the value of r is2007 · MCQ
Let $R$ denote the set of all real numbers. Let $a_{i}, b_{i} \in R$ for $i \in {1, 2, 3}$ . Define the functions $f : R \to R$ , $g : R \to R$ , and $h : R \to R$ by $f (x) = a_{1} + 10 x + a_{2} x^{2} + a_{3} x^{3} + x^{4} g (x) = b_{1} + 3 x + b_{2} x^{2} + b_{3} x^{3} + x^{4} h (x) = f (x + 1) - g (x + 2)$ …2025 · MCQ
Let $a = 32$ and $b = \frac{1}{5 ^{1/6} 6}$ . If $x, y \in R$ are such that $3 x + 2 y = lo g_{a} (18)^{\frac{5}{4}} and 2 x - y = lo g_{b} (1080),$ then $4 x + 5 y$ …2024 · Numerical
The product of all positive real values of $x$ satisfying the equation $x^{(16 (l o g_{5} x)^{3} - 68 l o g_{5} x)} = 5^{- 16}$ is .2022 · Numerical
For x $\in$ R, the number of real roots of the equation $3 x^{2} - 4 x^{2} - 1 + x - 1 = 0$ is .2021 · Numerical
Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x $-$ 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x2 $-$ 20x + 2020. Then the value of ac(a $-$ c) + ad(a $-$ d) + bc(b $-$ …2020 · MCQ
Let $α$ and $β$ be the roots of $x^{2} - x - 1 = 0$ , with $α$ > $β$ . For all positive integers n, define $a_{n} = \frac{α ^{n} - β ^{n}}{α - β}, n \geq 1 b_{1} = 1 an d b_{n} = a_{n - 1} + a_{n + 1}, n \geq 2$ …2019 · Multiple correct
Let a, b, c three non-zero real numbers such that the equation $3 a cos x + 2 b sin x = c, x \in [- \frac{π}{2}, \frac{π}{2}]$ , has two distinct real roots $α$ and $β$ with $\alpha + \beta = {\pi \over…2018 · Numerical