Question

if the sum of zeros of the polynomial
kx square - 5 x square - 11 x - 3 is 5/3 then find k
​

Answer 1

   Answer:

   $k=\frac{58}{5}$

   Step-by-step explanation:

   Let the polynomial be $f(x) = kx^{2} - 5x^{2} -11x -3$

⇒ We can write this as

   $f(x) = (k-5)x^{2} - 11x - 3$

   We know that the sum of roots of a polynomial, of the form $ax^{2} +bx +c = 0$,

   is $\frac{-b}{a}$

⇒ Sum of roots of $f(x)$ = $\frac{-(-11)}{k-5}$ = $\frac{5}{3}$

⇒ $\frac{5}{3} = \frac{11}{k-5}$

⇒ $5(k-5) = 11(3)$

⇒ $5k - 25 = 33$

⇒ $5k = 58$

∴ $k=\frac{58}{5}$