Math, asked by sahidregisow66, 5 hours ago

If α and β are zeroes of 3x2 – 2x – 6, then find α

2 + β

2

.​

Answers

Answered by negivardhan993
1

Explanation:

\textsf{We know that in a quadratic polynomial of form ax^2 + bx + c}\textsf{We know that in a quadratic polynomial of form}  \mathsf{ax^2 + bx + c} \textsf{with roots} \: \alpha \textsf{and} \: \beta,

\mathsf{\alpha +\beta=\frac{-b}{a}}\: \textsf {and} \: \mathsf{\alpha\beta=\frac{c}{a}}

\textsf{In the given polynomial, a = 3, b = -2 and c = -6, and we wish to find }\alpha^2 + \beta^2.

\alpha^2 + \beta^2 = (\alpha + \beta)^2-2\alpha\beta

\mathsf{=(\frac{2}{3})^2- (2\times\frac{-6}{3}})

\mathsf{=\frac{4}{9}-(2\times-2)}

\mathsf{=\frac{4}{9}+4 = \frac{4+36}{9}}

\mathsf={\frac{40}{9}}

Answer: 40/9

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