JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Hard

1 of 1

Application +4 | -1

Let

a, b, c

be the sides of a triangle. No two of them are equal and

\lambda \in R

. If the roots of the equation

x^2+2(a+b+c) x+3 \lambda(a b+b c+c a)=0

are real, then

View answer and explanation

Correct option: A

\lambda<\frac{4}{3}

Option A (

\lambda<\frac{4}{3}

) is correct because the discriminant of the quadratic equation must be non-negative, leading to the inequality

\lambda < \frac{4}{3}

More Questions from QUADRATIC EQUATIONS

Practice All Chapter MCQs →

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

\alpha ,\beta

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

\alpha < 1 < \beta ,

\alpha ,\;\beta

{x^2} - px + q = 0

{\alpha _1},{\beta _1}

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

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

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

x

a

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

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

\;a \ne 0,

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

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