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Question
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
Solution
Let the first root be α, then the second root will be 6a
Sum of roots = `(-"b")/"a"`
`=> "a" + 6"a" = 14/"p"`
`=> 7"a" = 14/"p"`
`=> "a" = 2/"p"`
Product of roots = `"c"/"a"`
`=> "a"xx 6"a" = 8/"p"`
`=> 6"a"^2 = 8/"p"`
`=> 6(2/"p")^2 = 8/"p"`
`=>6xx4/"p"^2= 8/"p"`
`=>"p"=6xx4/8`
`=> "p" = 3`
Hence, the value of p is 3.
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