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.
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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.
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