Question

If alpha and beta are zeroes of the polynomial P(X)=6x2-5x+k, such that alpha- beta =1/6, find the value of k

Answer 1

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

Hope this helps......

Answer 2

Answer:

a=alpha

b= beta

so...

a+b = 5/6

and

a-b =1/6

so...

a+b=5/6

a-b =1/6

_______

2a. =1

a=1/2

p(x)=6x^2-5x+k

p(a)=6(1/2)^2-5(1/2)+k

0 =6(1/4)-5/2+k

0 =(3/2)-(5/2)+k

0=-(2/2)+k

k-1=0

so. k=1

this one is the easier method

Step-by-step explanation: