10th Class Mathematics Solved Paper - Mathematics-2016 Outside Delhi Set-I

  • question_answer 5) If \[5\] is a root of the quadratic equation \[2{{x}^{2}}+px-15=0\] and the quadratic equation \[p({{x}^{2}}+x)k=0\] has equal roots, find the value of k.

    Answer:

    Given, \[5\] is a root of \[2{{x}^{2}}+px-15=0\]
    then,     \[f(-5)=2{{(-5)}^{2}}+p(-5)-15=0\]
                        \[50-5p-15=0\]
                 \[35-5p=0\]
                         \[5p=35\]
                           \[p=7\]
    Now, putting the value of p, in, \[p({{x}^{2}}+x)+k=0\]
    we get               \[7{{x}^{2}}+7x+k=0\]
    Now,                 \[D={{b}^{2}}-4ac=0\] (\[\because \] has the equal roots)
    then,                 \[49-28k=0\]
                            \[28k=49\]
                            \[k=\frac{49}{28}=\frac{7}{4}\]


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