Question

Find the equation whose roots are three times the reciprocals of the roots of 4x2 – 15x + 12 = 0.
4x2 – 15x + 9 = 0
108x2 - 45x + 4 = 0
12x – 15x + 4 = 0
4x2 - 15x + 12 = 0​

Answer 1

Answer:

F(x) = 4 x2 - 3x - 1

Let α , β be the zeros of f(x)

Using the relation between the zeros and coefficients

Sum of zeros =

α+ β= -b/a

α + β = 3/4........i

Product of zeros,

αβ = c/ a

αβ = -1/4.........ii

Now let the zeros of the new quadratic equation be 1/α & 1/β

Then sum of zeros = 1/α +1/β

= α+β/αβ = 3/4*4/-1 (from i and ii)

= -3

Product of zeros = 1/α*1/β

= 1/αβ = 1*-1/4 = -4

Therefire the equation is

x2+3x-4

Hope this helps..

Step-by-step explanation:

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