Question

For what value of k, x = a is a solution of the equation
x2 – (a + b) x + k = 0.

Answer 1

Note:

• The possible values of unknown (variable) for which the equation is satisfied are called its solutions or roots .

• If x = a is a solution of any equation in x , then it must satisfy the given equation otherwise it's not a solution (root) of the equation.

Answer:

k = ab

Solution:

The given quadratic equation is :

x2 – (a + b) x + k = 0 ---------(1)

It is given that , x = a is a solution of the given quadratic equation.

Thus ,

x = a must satisfy eq-(1)

=> x² - (a+b)x + k = 0

=> a² - (a+b)a + k = 0

=> a² - a² - ab + k = 0

=> k - ab = 0

=> k = ab

Hence,

The required value of k is ab.

Answer 2

$\huge{\boxed{\red{\star\;Answer}}}$

$\large{\underline{\blue{\star\;Note}}}$

• x = 'a' is said to be a root of the equation if 'a' satisfies the given equation

Given equation ,

• x^2 - (a+b)x + k = 0

Given a is a root

Substituting value of x as a ,

• a^2 -(a+b)a + k = 0
• a^2 - a^2 -ab + k = 0
• k = ab

$\large{\boxed{\green{\;The\;value\;of\;k\;is\;ab}}}$