Question

for what value of k, the zero of a quadratic polynomial p(x) =2x square +9x +(k square +2 k-1) are negative reciprocal of each other​

Answer 1

Given :- for what value of k, the zero of a quadratic polynomial p(x) =2x square +9x +(k square +2 k-1) are negative reciprocal of each other ?

Solution :-

p(x) = 2x² + 9x + (k² + 2k - 1)

we know that, for a quadratic polynomial p(x) = ax² + bx + c ,

• sum of roots = (-b/a)
• product of roots = c/a

since roots are negative reciprocal of each other . so,

→ m * -1/m = c/a

→ -1 = c/a

→ k² + 2k - 1 / 2 = -1

→ k² + 2k - 1 = (-2)

→ k² + 2k + 1 = 0

→ (k + 1)² = 0

→ k = (-1) (Ans.)

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