Question

Find what value of k, -3 is a zero of a polynomial ${x^2} + 11x + k$

Answer 1

Hint: Here, we will proceed by finding the value of k by putting the value of x= -3 as given in the question that it is a zero of the given polynomial. Then simply put the value of K in the given polynomial and solve it.

Complete step-by-step answer:
Now, we have to calculate this question by using a quadratic equation that is $a{x^2} + bx + c = 0$ in terms of x where A,B and C are constants. By using this formula, we will get our required answer.
Polynomial function – A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x. We can give a general definition of a polynomial, and define its degrees.
Given equation is:
${x^2} + 11x + k$ =0; where x = -3
Putting the value of x = -3, we will get,
${\left( { - 3} \right)^2} + 11\left( { - 3} \right) + k = 0$
$\therefore {\text{ }}$ k = 24
Now, by using quadratic equation we will get,
$
  {\text{ = }}{{\text{x}}^2} + 11x{\text{ + 24 = 0}} \\
  {\text{ = }}{{\text{x}}^2}{\text{ + 8x + 3x + 24 = 0}} \\
   = x\left( {x + 8} \right) + 3\left( {x + 8} \right) \\
   = \left( {x + 3} \right)\left( {x + 8} \right) = 0 \\
 $
Hence,
X=-3 and -8

Note: During solving this question, one can make many little mistakes which can lead him/her to the wrong answer one such mistake is that during splitting the middle term in order to have the correct solution one can split it in the wrong way i.e. 11x= 9x+2x . So, it will not be solved further.