If both roots of the quadratic equation $(2 - x) (x + 1) = p$ are distinct and positive, then $p$ must lie in the interval

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Important Questions on Quadratic Equations

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 32

If two roots of the equation

(a - 1) {(x^{2} + x + 1)}^{2} - (a + 1) (x^{4} + x^{2} + 1) = 0

are real and distinct, then

' a'

lies in the interval

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 33

The equations

x^{3} + 5 x^{2} + p x + q = 0

and

x^{3} + 7 x^{2} + p x + r = 0

have two roots in common. If the third root of each equation is represented by

x_{1}

and

x_{2}

respectively, then the ordered pair

(x_{1}, x_{2})

is:

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 34

If

a, b, c

are real and

a^{2} + b^{2} + c^{2} = 1,

then all the values of

a b + b c + c a

lies in the interval

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-2>Q 38

If $α, β$ are roots of the equation $λ (x^{2} - x) + x + 5 = 0 .$ If $λ_{1}$ and $λ_{2}$ are the two values of $λ$ for which the roots $α, β$ are connected by the relation $\frac{α}{β} + \frac{β}{α} = 4,$ then the value of $(\frac{\frac{λ_{1}}{λ_{2}} + \frac{λ_{2}}{λ_{1}}}{14})$ is