Question

In the question if alpha and beta are the zeros of p(x)=6x2-5x+k such that alpha-beta =1/6, find the value of k. How the 7 step came?(i.e)(-5)square - 4(6)+k. Please can u explain.......

Answer 1

Answer:

k=1

Step-by-step explanation:

If a quadratic equation is of form ax²+bx+c = 0, the sum of roots = -b/a and product of roots = c/a.

The given equation p(x) = 6x² - 5x + k

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

sum of zeros = α + β = -b/a = 5/6

Product of zeroes = αβ = c/a = k/6

given

α - β = 1/6

Square on both sides

(α - β)² = 1/36

we know that (α - β)² = α² + β² - 2αβ = α² + β² + 2αβ - 4αβ

                                   = (α + β)² - 4αβ

=> (α + β)² - 4αβ = 1/36

=> (5/6)² - 4(k/6) = 1/36

=> 4k/6 = 25/36 - 1/36

=> 4k/6 = 24/36

=> k = 24/36 * 6/4 = 1.

I hope this helps.