Question

if m and n are zeroes of quadratic polynomial x2-(k-6)n+2(2k-1) find the k if m+n = 1/2 mn.​

Answer 1

Answer:-

Given Polynomial => x² - (k - 6)n + 2(2k - 1).

Let , a = 1 ; b = - (k - 6) ; c = 2(2k - 1)

We know that,

Sum of roots = - b/a

→ m + n = - [ - (k - 6) ]/1

→ m + n = k - 6 -- equation (1)

Product of the roots = c/a

→ mn = 2(2k - 1)/1

→ mn = 2(2k - 1) -- equation (2)

And also given that,

m + n = 1/2* mn

Putting values from equation (1) & (2) we get,

→ k - 6 = 1/2 * 2 * 2k - 1

→ k - 6 = 2k - 1

→ k - 2k = - 1 + 6

→ - k = 5

→ k = - 5.