Let $a,\,\,b,\,\,c$ be in an arithmetic progression. Let the centroid of the triangle with vertices $(a,c),\,\,\,(2,b)\,$ and $(a,\,\,b)$ be $\left( {\frac{{10}}{3},\,\,\,\frac{7}{3}} \right)$. If $\alpha ,\,\,\,\beta \,$ are the roots of the equation $a{x^2} + bx + 1 = 0$, then the value of ${\alpha ^2} + {\beta ^2} - \alpha \beta $ is

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

a,\,\,b,\,\,c

be in an arithmetic progression. Let the centroid of the triangle with vertices

(a,c),\,\,\,(2,b)\,

and

(a,\,\,b)

\left( {\frac{{10}}{3},\,\,\,\frac{7}{3}} \right)

. If

\alpha ,\,\,\,\beta \,

are the roots of the equation

a{x^2} + bx + 1 = 0

, then the value of

{\alpha ^2} + {\beta ^2} - \alpha \beta

View answer and explanation

Correct option: D

- \frac{{71}}{{256}}

Option D (

\frac{{ - 71}}{{256}}

) is correct because by using the centroid coordinates and the arithmetic progression property, we can find the values of a, b, and c, and then calculate the required expression using the roots of the quadratic equation.

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

More Questions from QUADRATIC EQUATIONS