Question

4. Find the value of k such that sum of
the roots of the quadratic equation
3x2 + (2k + 1)x - (k + 5) = 0 is equal to
the product of its roots.
.​

Answer 1

Answer: 4

Step-by-step explanation:

The given equation is 3x2 + (2k + 1)x - k - 5 = 0

Compare with ax2 + bx + c = 0, we get

a = 3, b = 2k + 1, c = - k - 5

∴Sum of the roots =

- b/a = - ( 2k + 1 )/3

and Product of the roots =

c/a = (- k - 5)/3 = - ( k + 5 )/3

According to question ,

∵ Sum of the roots = Product of the roots

∴

- ( 2k + 1 )/3 = - ( k + 5 )/3

⇒ 2k + 1 = k + 5

⇒ 2k - k = 5 - 1

⇒ k = 4.

Therefore , the value of k is 4 .