Question

if alpha and beta are the zeroes of the polynomial p(x)=6x^2-5x+k suck that alpha-beta=1 by 6 find k

Answer 1

Answer:

Given:

• alpha and beta are the zeroes polynomial p(x)=6x^2-5x+k

• and alpha-beta=1 by 6

To find:

•   The value of 'k'

Pre-requisite Knowledge :

if α and β are the zeros.

•  α + β = -b/a

• α* β = c/a

Solving question:

 We are given α and β as zeros of the polynomial.Therefore we can use the above mentioned formulas to find the answer.Substitute the values in the equation.

Solution:

a = 6 ; b = -5 ; c = k

α + β = -b/a

⇒  α + β = -(-5)/6

⇒  α + β = 5/6 ............equ(1)

α * β = c/a = k/6 ............equ(3)

α - β = 1/6 (given) ..........equ(2)

add equ(1) and equ(2)

α + β = 5/6

α - β = 1/6

.........................

we get, 2α = 5/6 + 1/6

or,  2α = 6/6

⇒ α = 1/2

substitute in equ(2)

α - β = 1/6

⇒ 1/2 -β = 1/6

⇒ β = 1/2 -1/6

or, β = (3-1)/6 [after taking L.C.M]

or, β = 2/6 = 1/3

substitute in equ(3)

α * β = c/a = k/6  

1/2 * 1/3 = k/6

or, 1/6 = k/6

or, k = 1

∴ The value of 'k' is 1