Question

3. For what value of k does the quadratic equation K-5x +2k-5x+2=0 have equalroots? ​

Answer 1

Answer:

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 ;

(k-5)x² + 2(k-5)x + 2 = 0

Clearly , we have ;

a = k-5

b = 2(k-5)

c = 2

We know that ,

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

=> D = 0

=> [2(k-5)]² - 4•(x-5)•2 = 0

=> 4(k-5)² - 4•2(k-5) = 0

=> 4(k-5)•(k-5-2) = 0

=> (k-5)(k-7) = 0

=> k = 5 , 7

Hence,

The required values of k are 5 and 7 .