Question

If the product of the roots of 5x2 - 4x + 2 + m(4x2-2x-1) = 0 is 3, then ​

Answer 1

Answer:

- 1

Step-by-step explanation:

Notice that the given equation is not in standard form(ax² + bx + c=0),  so we first need to convert this in standard form:

Given eq:

   ⇒ 5x² - 4x + 2 + m(4x² - 2x - 1) = 0

   ⇒ 5x² - 4x + 2 + 4mx² - 2mx - m = 0

   ⇒ 5x² + 4mx² - 4x - 2mx + 2 - m = 0

   ⇒ (5 + 4m)x² - (4 + 2m)x + (2 - m) = 0

   For ax² + bx + c = 0,    product of roots = c/a

In this question,

           a = (5 + 4m)     ;   c = (2 - m)

Given, product of root = 3

∴ c/a = 3

⇒ (2 - m)/(5 + 4m) = 3

⇒ 2 - m = 15 + 12m

⇒ 2 - 15 = 12m + m

⇒ - 13 = 13m

⇒ -1 = m

         therefore the required value of m is - 1