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  • If the orthocentre of the triangle, whose vertices are and <img alt="(3,1)" src="https://entran

If the orthocentre of the triangle, whose vertices are (1,2)(2,3) and (3,1) is (\alpha, \beta), then the quadratic equation whose roots are \alpha+4 \beta and 4 \alpha+\beta, is

Option: 1

x^2-20 x+99=0


Option: 2

x^2-19 x+90=0


Option: 3

x^2-22 x+120=0


Option: 4

x^2-18 x+80=0


Answers (1)

best_answer

equation of A D: x-2 y+3=0

equation of  C E: x+y-4=0

orthocenter (\alpha, \beta) is \left(\frac{5}{3}, \frac{7}{3}\right)$ $\alpha+4 \beta=11$ and $4 \alpha+\beta=9

Quadratic equation is
$$ \begin{aligned} & x^2-(11+9) x+(11 \times 9)=0 \\ & \Rightarrow x^2-20 x+99=0 \end{aligned}

Posted by

Shailly goel

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