Question

If a and b are the zeros of polynomial 6x^2-5x+k such that -b=1/6. Find the value of k.

Answer 1

Hola!!!

$- b = \frac{1}{6} \\ b = \frac{ - 1}{6}$

sum of zeroes=-b/a

$a + b = - \frac{b}{a}$

$a + - \frac{1}{6} = \frac{5}{6} \\ a = \frac{7}{6}$

now,

product of zeroes=c/a

$ab = \frac{k}{6} \\ \frac{7}{6} \times \frac{ - 1}{6} = \frac{k}{6} \\ \frac{ - 7}{36} \times 6 = k \\ k = \frac{ - 7}{6}$

Therefore the value of k os

$\frac{ - 7}{6}$

HOPE IT HELPS YOU ❤✨