Question

find the value of k for which the quadratic equation X square - 3 x + K equal to zero has equal roots.

Answer 1

For equal root D=0,Here,D=b^2-4ac,D=(-3)^2-4×1×k,D=9-4k,9-4K=0,K=9/4

Answer 2

Question:

Find the value of k for which the quadratic equation x² - 3x + k = 0 has equal roots.

Answer:

k = ± 3/2

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 .

• 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 - 3x + k = 0 .

Clearly , we have ;

a = 1

b = -3

c = k

We know that ,

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

=> D = 0

=> (-3)² - 4•1•k= 0

=> 9 - 4k = 0

=> 4k = 9

=> k² = 9/4

=> k = √(9/4)

=> k = ± 3/2

Hence,

Hence,The required values of k are ± 3/2 .