If One Zero of the Quadratic Polynomial p(x) = 4x² – 8xk – 9 is Negative of the Other Find the Value of k

Answer: According to the question, if p(x)=0 (i.e. 4x² – 8xk – 9 = 0) then the roots of the quadratic equation are of same value but different sign. Now, we know that, if ax² + bx + c = 0 is a quadratic equation and its roots are ‘p’ and ‘q’ then,

p + q = – b/a & pq = c/a

   Here, let us assume that the roots of the given equation are ‘m’ and ‘n’. According to the problem,

m = -n

or, m + n = 0 …….. equation (i)

 By the aforesaid formula, we can say that,

              m + n = – (-8k)/4

m + n = 2k

2k = 0 [putting, m + n = 0 from equation (i)]

 k = 0

Therefore the value of k is 0.