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Class-9»Maths

IF THE ROOT OF EQUATION px^2 -14x + 8 = 0 IS 6 TIMES THE OTHER THEN , find the value of p ?

$Given {px}^{2} - 14 x + 8 = 0 Let α, β are the roots of the equation β = 6 α we know that sum of the roots= \frac{- b}{a} product of the roots= \frac{c}{a} here a=p,b=-14,c=8 \Rightarrow α + β = \frac{14}{p} α β = \frac{8}{p} \Rightarrow α + 6 α = \frac{14}{p} \Rightarrow 7 α = \frac{14}{p} \Rightarrow α = \frac{2}{p} α β = \frac{8}{p} \Rightarrow α (6 α) = \frac{8}{p} \Rightarrow 6 α^{2} = \frac{8}{p} \Rightarrow 3 α^{2} = \frac{4}{p} \Rightarrow 3 (\frac{2}{p})^{2} = \frac{4}{p} \Rightarrow 3 (\frac{4}{p^{2}}) = \frac{4}{p} \Rightarrow p = 3$

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