Question

The sum and product of zeroes of polynomial f(x) =4x2 - 27x+3k are equal. find the value of k

Answer 1

k=9 hope it will help u

Answer 2

Answer: The value of k is 9.

Step-by-step explanation:

Let a and b are the zeroes of the given polynomial f(x) =4x2 - 27x+3k,

Since, the sum of the zeroes,

$a+b=\frac{\text{Coefficient of x}}{\text{Coefficient of } x^2}$

$a+b=-\frac{-27}{4}=\frac{27}{4}$

Now, the product of the zeroes,

$ab=\frac{\text{Constant term}}{\text{Coefficient of } x^2}$

$\implies ab = \frac{3k}{4}$

According to the question,

a+b = ab

⇒ $\frac{27}{4}=\frac{3k}{4}$

⇒ $27 = 3k \implies k = 9$

Hence, The value of k is 9.