JEE MATHEMATICS MCQ: THEORY OF EQUATION

1 Easy

1 of 1

Analyzing +4 | -1

If the equations

x^2+2 x+3=0

and

a x^2+b x+c=0

a, b, c \in R

have a common root, then

a: b: c

View answer and explanation

Correct option: D

1: 2: 3

Option D (

1: 2: 3

) is correct because the two equations have a common root, and since the roots of the first equation are imaginary, both roots must be common, making the equations proportional.

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The maximum number of real roots of the equation

{x^{2n}} - 1 = 0

is The number of roots of the equation

\frac{1}{x}+\frac{1}{\sqrt{\left(1-x^2\right)}}=\frac{35}{12}

is How many real solutions does the equation

x^7+14 x^5+16 x^3+30 x-560=0

have? If

x_1, x_2, x_3, \ldots, x_n

are the roots of the equation

x^n+a x+b=0

, the value of

\left(x_1-x_2\right)\left(x_1-x_3\right)\left(x_1-x_4\right) \ldots\left(x_1-x_n\right)

is The polynomials

P(x)=k x^3+3 x^2-3

and

Q(x)=2 x^3-5 x+k

, when divided by

(x-4)

leave the same remainder, then

k

is equal to: If

{\left( {x - 1} \right)^3}

is a factor of

{x^4} + a{x^3} + b{x^2} + cx - 1,

then the other factor is