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  • Stuck here, help me understand: - Integral Calculus - JEE Main-10

What is the perfect square form of  x^{2}+kx+7?

  • Option 1)

    (x-k/2)^{2}+7

  • Option 2)

    (x+k/2)^{2}+7

  • Option 3)

    (x+k/2)^{2}+7-k^{2}

  • Option 4)

    (x+k/2)^{2}+7-k^{2}/4

 

Answers (1)

best_answer

As we have learned

Integration by perfect square method -

ax^{2}+bx+c=a\left [ x^{2}+\frac{bx}{a}+\frac{c}{a} \right ]=a\left [ \left ( x+\frac{b}{2a} \right )^{2}+\frac{c}{a}-\frac{b^{2}}{4a^{2}} \right ]

- wherein

Make the coefficient of x^{2} +ve one . 

 

x^{2}+kx+7 \Rightarrow x^{2}+2*k/2*x+k^{2}/4+7-k^{2}/4

\left ( x+ k/2 \right )^{2}+\left ( 7-k^{2}/ 4\right ) 

 

 

 

 


Option 1)

(x-k/2)^{2}+7

This is incorrect

Option 2)

(x+k/2)^{2}+7

This is incorrect

Option 3)

(x+k/2)^{2}+7-k^{2}

This is incorrect

Option 4)

(x+k/2)^{2}+7-k^{2}/4

This is correct

Posted by

gaurav

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