Question

If one zero of a quadratic polynomial: \[{x^2} + 3x + k\] is \[2\] find the value of \[k\]

Answer 1

Hint: Here, we are given a quadratic polynomial and one of its zero and we are asked to find the value of \[k\] .So we will proceed in this question by finding the value of \[k\] and we will find it by substituting the value of \[x = 2\] as it is given in the question that it is a zero of the given polynomial so it must satisfy the given quadratic equation.

Complete step by step answer:
Given quadratic equation is:
\[{x^2} + 3x + k{\text{ }} - - - \left( 1 \right)\]
And one of the zeros of the quadratic polynomial is \[2\]
And we are asked to find the value of \[k\]
Now, it is given that \[2\] is the zero of the given quadratic equation.
It means that when we put \[2\] at the place of \[x\] it gives the value \[0\] as it satisfies the given quadratic equation.
So, let \[x = 2\]
Now, substitute the value of \[x\] in equation \[\left( 1 \right)\] we will get
\[{\left( 2 \right)^2} + 3\left( 2 \right) + k = 0\]
On simplifying it, we get
\[4 + 6 + k = 0\]
\[ \Rightarrow 10 + k = 0\]
Subtract \[10\] from both sides, we get
\[k = - 10\]
Hence, the value of \[k = - 10\].

Note:
It means that when we put the value of \[k = - 10\] in the given quadratic equation and find its zeros by using factorization method or by any method, one of its zeros will be \[2\] We can also verify it and can also find the second zeros of the quadratic polynomial after finding the value of \[k\]
As after putting the value of \[k\] , quadratic polynomial becomes
\[{x^2} + 3x - 10\]
Using the factorization method, we can find its zeros.
So, it can be written as
\[{x^2} + 5x - 2x - 10 = 0\]
\[ \Rightarrow x\left( {x + 5} \right) - 2\left( {x + 5} \right) = 0\]
After simplification, we get
\[ \Rightarrow \left( {x - 2} \right)\left( {x + 5} \right) = 0\]
\[ \Rightarrow x = 2,{\text{ }}x = - 5\]
Hence, we can see that one of the zeros of quadratic polynomial is \[2\] and another zero is \[ - 5\]