Question

If zeroes of x²-kx+6 are in the ratio 2:3, find the value of k.

Answer 1

p(x) = x² - kx + 6 = 0
Here on comparing the polynomial p ( x ) with the form ax² + bx + c = 0
a = 1 , b = -k & c = 6
Now, the ratio of the zeroes of the polynomial p ( x ) = 2 : 3.
Let the common multiple of the ratio be 'y'.

So,the ratio of the p ( x ) = 2y : 3y

Now, the sum of zeroes = -b / a
2y + 3y = - ( - k ) / 1
5y = k......................(1)

Now, the product of zeroes = c/a
2y * 3y = 6 / 1
6y² = 6
y²  =  1
y = √1
y = +- 1

Now,
we know that 
5y = k ..............from 1
So,
k = 5 * =- 1
So,
k = +- 5

Hope this helps you
# Dhruvsh

Answer 2

I hope this will help you.