Question

2xsquare-Kx+1 , find K for equal roots.

Answer 1

Answer :

k = ± 2√2

Note :

★ The discriminant , D of the quadratic polynomial ax² + bx + c is given by ;

D = b² - 4ac

★ If D = 0 , then the zeros are real and equal .

★ If D > 0 , then the zeros are real and distinct .

★ If D < 0 , then the zeros are unreal (imaginary) .

Solution :

Here ,

The given quadratic polynomial is ;

2x² - kx + 1 .

Comparing the given quadratic polynomial with the general quadratic polynomial ax² + bx + c , we have ;

a = 2

b = -k

c = 1

We know that. ,

For real and equal zeros , the discriminant of the polynomial is zero .

Thus ,

=> D = 0

=> b² - 4ac = 0

=> (-k)² - 4•2•1 = 0

=> k² - 8 = 0

=> k² = 8

=> k = √8

=> k = ± 2√2

Hence , k = ± 2√2 .