# If 1 is the zero of $f\left( x \right) = k{x^2} - 3kx + 3k - 1$ then the value(s) of $k$ is

Answer

Verified

361.2k+ views

Hint- Use the concept that for a quadratic equation or any function the zero of that quadratic equation or the function will always satisfy the equation or the value of that function will be zero.

Complete step-by-step solution -

Given that the function is $f\left( x \right) = k{x^2} - 3kx + 3k - 1$

And 1 is the zero of the equation. So by the help of hint we have

$f\left( 1 \right) = 0$

So proceeding forward with the function, we have

$

f\left( {x = 1} \right) = {\left. {k{x^2} - 3kx + 3k - 1} \right|_{x = 1}} = 0 \\

\Rightarrow f\left( 1 \right) = k{\left( 1 \right)^2} - 3k\left( 1 \right) + 3\left( 1 \right) - 1 = 0 \\

\Rightarrow k - 3k + 3 - 1 = 0 \\

$

Proceeding forward in order to find the value of $k$

\[ \Rightarrow k - 3k + 3 - 1 = 0 \\

\Rightarrow - 2k + 2 = 0 \\

\Rightarrow - 2k = - 2 \\

\Rightarrow k = 1 \\

\]

Hence, the value of k is 1.

Note- A zero of a function is an input value to the function that produces an output of 0. Also remember that roots of an equation are also called its zero. If one of the roots of the function is given, other roots can also be found out easily. Remember these points while solving such problems.

Complete step-by-step solution -

Given that the function is $f\left( x \right) = k{x^2} - 3kx + 3k - 1$

And 1 is the zero of the equation. So by the help of hint we have

$f\left( 1 \right) = 0$

So proceeding forward with the function, we have

$

f\left( {x = 1} \right) = {\left. {k{x^2} - 3kx + 3k - 1} \right|_{x = 1}} = 0 \\

\Rightarrow f\left( 1 \right) = k{\left( 1 \right)^2} - 3k\left( 1 \right) + 3\left( 1 \right) - 1 = 0 \\

\Rightarrow k - 3k + 3 - 1 = 0 \\

$

Proceeding forward in order to find the value of $k$

\[ \Rightarrow k - 3k + 3 - 1 = 0 \\

\Rightarrow - 2k + 2 = 0 \\

\Rightarrow - 2k = - 2 \\

\Rightarrow k = 1 \\

\]

Hence, the value of k is 1.

Note- A zero of a function is an input value to the function that produces an output of 0. Also remember that roots of an equation are also called its zero. If one of the roots of the function is given, other roots can also be found out easily. Remember these points while solving such problems.

Last updated date: 27th Sep 2023

â€¢

Total views: 361.2k

â€¢

Views today: 3.61k

Recently Updated Pages

What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

What is the basic unit of classification class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers