Question

Solution for , find the value of k , if the roots of x square +kx+12=0are in the ratio 1:3

Answer 1

Let X and 3X are the two zeroes of the given quadratic polynomial.



X² + KX + 12 = 0


Here,

a = 1 , b = k and c = 12.




Product of zeroes = c/a


X × 3X = 12



3X² = 12



X² = 4


X = √4


X = 2.



First zero = x = 2


And,


Second zero = 3x = 3 × 2 = 6.




Sum of zeroes = -b/a


x + 3x = -k


2 + 6 = -k


8 = - k


K = -8