Question

find the value of k for which the quadratic equation x^2-x+k=0 has equal roots

Answer 1

Given quadratic equation
x^2 + 5x + k = 0
and we have been given roots are not equal. If roots are real then
So discriminant will be greater than zero.
D>0
=>b^2 - 4ac >0
=> (5)^2 - 4 (1)(k)>0
=>25 - 4k > 0
=> 4k<25
=>k<25/4
=>k<6.25 ANSWER

Answer 2

Question:

Find the value of k for which the quadratic equation x² - x + k = 0 has equal roots.

Answer:

k = 1/4

Note:

• An equation of degree 2 is know as quadratic equation .

• Roots of an equation is defined as the possible values of the unknown (variable) for which the equation is satisfied.

• The maximum number of roots of an equation will be equal to its degree.

• A quadratic equation has atmost two roots.

• The general form of a quadratic equation is given as , ax² + bx + c = 0 .

• The discriminant of the quadratic equation is given as , D = b² - 4ac .

• If D = 0 , then the quadratic equation would have real and equal roots .

• If D > 0 , then the quadratic equation would have real and distinct roots .

• If D < 0 , then the quadratic equation would have imaginary roots .

Solution:

The given quadratic equation is ;

x² - x + k = 0

Clearly , we have ;

a = 1

b = -1

c = k

We know that ,

The quadratic equation will have real and equal roots if its discriminant is equal to zero .

=> D = 0

=> (-1)² - 4•1•k = 0

=> 1 - 4•1•k = 0

=> 1 - 4k = 0

=> 4k = 1

=> k = 1/4

Hence,

The required values of k is 1/4 .