Example Question 10

Example corresponding to question 10 in algebra_4.

Example 1


If $x^2-4x+4=0$, then $x^3+x^2+1=?$

  1. $5$


  2. $13$


  3. $3$


  4. $-3$


  5. $1$

Solution


  1. From the 5 possible answers, we need to evaluate the expression $x^3+x^2+1$ for a certain value of x which can only be the solution of the given equation. So we first solve the given quadratic equation. Note that the left hand term of the equation can be factored as follows

    $x^2-4x+4=(x-2)(x-2)=(x-2)^2$


  2. Hence the given equation is equivalent to the equation

    $(x-2)^2=0$ and its solution is $x = 2$

  3. We now substitute x by 2 in the expression $x^3+x^2+1$ and evaluate it.

    $(2)^3+(2)^2+1=8+4+1=13$

    Answer B