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  • Find the value of p, for which one root of the quadratic equation   is 6 times the other.   <div

Find the value of p, for which one root of the quadratic equation px^2 - 14x + 8 = 0  is 6 times the other.

 

 

 

 
 
 
 
 

Answers (1)

Given : Quadratic equation \Rightarrow px^2-14x+8

Find roots such that \alpha = 6\beta

We know that  

\alpha + \beta= -\frac{b}{a} \; \; \; \; -(i)

6\beta + \beta= -\frac{(-14)}{p} \;\;\;\;\;\;(\because \alpha = 6\beta)

\Rightarrow 7\beta = \frac{14}{p}

\Rightarrow \beta = \frac{2}{p}

\alpha \beta =\frac{c}{a}

\Rightarrow 6\beta^2 =\frac{8}{p}

\Rightarrow 6 \left ( \frac{2}{p} \right )^2 =\frac{8}{p}\;\;\;\;\;\;\;\left(\because \beta = \frac{2}{p} \right )

\Rightarrow 6 \times \frac{4}{p^2} =\frac{8}{p}

\Rightarrow p=3

Posted by

Ravindra Pindel

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