Question

If one find the value k zero of the polynomial 2x2-5x-(2k+1)

Answer 1

Answer:

k = -33/16

Step-by-step explanation:

Find Value of k if roots are equal

2x² -5x -(2k+1) = 0

For Roots to be equal

D = b² - 4ac = 0  for ax² + bx + c

here a = 2  , b = -5   c = -(2k + 1)

=> (-5)² - 4(2)(-(2k+1)) = 0

=> 25 + 8(2k + 1) = 0

=> 25 + 16k + 8 = 0

=> 16k = -33

=> k = -33/16

Putting k = -33/16

2x² -5x -(2(-33/16) + 1)  = 0

=> 2x² - 5x - (-33/8 + 1) = 0

=> 2x² - 5x - (-25/8)= 0

=>  2x² - 5x + 25/8 = 0

=> 2x² -5x/2 - 5x/2 + 25/8 = 0

=> √2x(√2x - 5/2√2) - (5/2√2)(√2x - 5/2√2) = 0

=> (√2x - 5/2√2)(√2x - 5/2√2) = 0

=> (√2x - 5/2√2)² = 0

=> √2x - 5/2√2 = 0

=> √2x = 5/2√2

=> x = 5/4