Question

Find k if one zero of polynomial 14x^2 - (k^2- 5k + 6)x + 5 is negative of the other.​

Answer 1

If the given condition is true, the sum of zeroes should be equal to 0

If zeroes are ß, -ß

Sum = ß - ß = 0

Thus, we know:

Sum of zeroes = -b/a

=> (k² - 5k + 6)/14 = 0

=> k² - 5k + 6 = 0

=> k² - 2k - 3k + 6 = 0

=> k(k - 2) - 3(k - 2) = 0

=> (k - 3) (k - 2) = 0

=> k = 2, 3