JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

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Analyzing +4 | -1

Let

\alpha, \beta

be the roots of the equation

a_1 x^2+2 b_1 x+c_1=0

and

\gamma, \delta

be the roots of

a_2 x^2+2 b_2 x+c_2=0

. If the four points

A(\alpha, 0), B(\beta, 0), C(\gamma, 0)

and

D(\delta, 0)

are such that the sum of the ratios in which

C

and

D

divide

A B

is zero, then

a_1 c_2+a_2 c_1

View answer and explanation

Correct option: A

2 b_1 b_2

Option A (

2 b_1 b_2

) is correct because the given condition about the ratios in which C and D divide AB leads to this relationship between the coefficients of the quadratic equations.

More Questions from QUADRATIC EQUATIONS

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The solution of the equation

\log _7 \log _5(\sqrt{x+5}+\sqrt{x})=0

is If

\alpha ,\beta

are the roots of

{x^2} - 3x + a = 0,a \in R

and

\alpha < 1 < \beta ,

then If

\alpha ,\;\beta

be the roots of the equation

{x^2} - px + q = 0

and

{\alpha _1},{\beta _1}

be the roots of the equation

{x^2} - qx + p = 0,

then the equation whose roots are

\frac{1}{{{\alpha _1}\beta }} + \frac{1}{{\alpha {\beta _1}}}\mathrm{and}\;\frac{1}{{\alpha {\alpha _1}}} + \frac{1}{{\beta {\beta _1}}},

is If

{x^2} + 4ax + 2 > 0

for all values of

x

, then

a

lies in the interval If

f\left( x \right) = a{x^2} + bx + c\;

and

\;f\left( { - 1} \right) < 1,f\left( 1 \right) > - 1,f\left( 3 \right) < - 4\;

and

\;a \ne 0,

then Root(s) of the equation

9{x^2} - 18\left| x \right| + 5 = 0

belonging to the domain of definition of the function

f\left( x \right) = \log \left( {{x^2} - x - 2} \right)

is (are)