Question

if a & b are zeroes of quadratic polynomial p(x)=xsquare+kx+45 such that (a_b)squar = 144 , find the value of k

Answer 1

LET A AND B BE THE ZEROES OF EQ.
THEN,
(A-B)^2 = 144
=> (A+B)^2 – 4AB = 144
=> (-b/a) – 4 x (c/a) = 144
In the given eqn,
x^2 + kx +45 in the form of ax^2 + bx + c
We get a = 1, b= k and c = 45
Replacing values,
(-k/1) – 4 x (45/1) = 144
=> k – 180 = 144
=> k = 324
=> k = 18