Question

if a and b are the zeroes pf the polynomial 6x2-5x+k such that alpha-bhitha=1/6 find the value of k

Answer 1

Answer:

Step-by-step explanation:

Let alpha = x and beta = y for clarity

We have,

=> x - y = 1/6

Squaring both sides we get :-

=> (x - y)² = 1/36

=> x² + y² - 2xy = 1/36

=> (x + y)² - 2xy - 2xy = 1/36

=> (-b/a)² - 4(c/a) = 1/36

=> b²/a² - 4c/a = 1/36

=> (b² - 4ac)/a² = 1/36

=> {(-5)² - 4(6)(k)}/(6)² = 1/36

=> (25 - 24k)/36 = 1/36

=> 25 - 24k = 36/36

=> -24k = 1 - 25

=> -24k = -24

=> k = 1