The given polynomial is
where a=1,b=k, c=30
Let the zeroes of this polynomial be m and n.
Then the sum of roots is
and the product of roots is
The square difference of the zeroes is given by the expression.
From the question, this difference is 169.
This implies that:
We substitute the values of k into the equation and solve for x.
The zeroes are given by;
This question is on finding the inverse of a 3×3 matrix
The general formula of finding a 3×3 matrix is given by;
where D is determinant
= 14 [ 40-2] - -13[ 15-10] + 0
=14  - [-65]+0
Diameter of the circle K = 20 units
Given that : EF = HG
Also, HG = 16 units
⇒ EF = 16 units
Now, any line drawn perpendicular to the chord always bisects the chord
⇒ KI will bisect the chord EF
⇒ EI = 8 units
Now, in ΔEIK using Pythagoras theorem we have :
⇒ EK² = 8² + 6²
⇒ EK² = 100
⇒ EK = 10 units
So, Radius of the circle K = 10 units
Now, Diameter of the circle K = 2 × 10
= 20 units