Question

If one zero of the the polynomial x² + 3x + k is 2, find k?​

Answer 1

Given :

 Quadratic polynomial 

$\implies\sf \red{ {x}^{2} + 3x + k}$

One of the root is 2

To find :

•  The value of k

Solution :

Let the given quadratic polynomial be

$\sf\implies \blue {f(x) = {x}^{2} + 3x + k}$

$\sf \bigstar\pink { \: Given \: one \: of \: the \: zero of \: the \: quadratic \: polynomial \: is \: 2.}$

$\sf \longrightarrow \green{Hence \: f(2) = 0}$

Put x = 2 in f(x), we get:-

$\implies\sf \bold \orange{f(2) = {2}^{2} + 3(2) + k}$

$\implies\sf \bold \orange{0 = 4 + 6 + k}$

$\implies \sf \bold \orange{0 = 10 + k}$

$\implies \sf \bold \green{k = - 10}$

Therefore, The value of k is -10.

Answer 2

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.

Solution :

Given quadratic equation is:

$\tt{\longrightarrow {x^2} + 3x + k \qquad\cdots \left( 1 \right)}$

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 ( 1 )we will get

$\tt{\longrightarrow {\left( 2 \right)^2} + 3\left( 2 \right) + k = 0 }$

$\tt{\longrightarrow 4 + 6 + k = 0}$

$\tt{ \longrightarrow 10 + k = 0}$

$\tt{\longrightarrow k = - 10}$

Hence, the value of k = - 10

$\qquad\rule{300pt}{1pt}$

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

$\tt{\longrightarrow{x^2} + 3x - 10}$

Using the factorization method, we can find its zeros.

So, it can be written as:

$\tt{\longrightarrow{x^2} + 5x - 2x - 10 = 0}$

$\tt{ \longrightarrow x\left( {x + 5} \right) - 2\left( {x + 5} \right) = 0}$

on simplifying we get :

$\tt{\longrightarrow \left( {x - 2} \right)\left( {x + 5} \right) = 0}$

$\tt{\longrightarrow x = 2,x = - 5 }$

Hence, we can see that one of the zeros of quadratic polynomial is 2and another zero is - 5

$\underline{\rule{300pt}{3pt}}$