JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(a , b , c\) be in 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 \(ax ^{2}+ bx +1=0\), then the value of \(\alpha^{2}+\beta^{2}-\alpha \beta\) is ....... .
- A \(\frac{71}{256}\)
- B \(\frac{69}{256}\)
- C \(-\frac{69}{256}\)
- D \(-\frac{71}{256}\)
Answer & Solution
Correct Answer
(D) \(-\frac{71}{256}\)
Step-by-step Solution
Detailed explanation
\(\frac{a+2+a}{3}=\frac{10}{3}\) \(a=4\) and \(\frac{c+b+b}{3}=\frac{7}{3}\) \(c+2 b=7\) also \(2 b=a+c\) \(2 b-a+2 b=7\) \(b=\frac{11}{4}\) now \(4 x ^{2}+\frac{11}{4} x +1=0 (0=\alpha \,And \, \beta)\) \(\alpha^{2}+\beta^{2}-\alpha \beta=(\alpha+\beta)^{2}-3 \alpha \beta\)…
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