Question

9. Find a quadratic equation whose roots are the reciprocal of the roots of the equation 4x2 -3x -1 = 0

Answer 1

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.. Plz mark as brainliest.....

Answer 2

Solution :

Given Quadratic equation

4x² - 3x - 1 = 0

=> 4x² - 4x + 1x - 1 = 0

=> 4x( x - 1 ) + 1( x - 1 ) = 0

=> ( x - 1 )( 4x + 1 ) = 0

x - 1 = 0 or 4x + 1 = 0

x = 1 or x = -1/4

ii ) Quadratic equation whose

roots are reciprocals of 1 and (-1/4)

Therefore ,

Roots are 1 , - 4

Sum of the roots = 1 -4 = -3

Product of the roots = 1 × ( -4 ) = -4

Required Quadratic equation ,

x² - ( sum of the roots )x + product

of the roots = 0

=> x² - ( -3 )x + ( -4 ) = 0

=> x² + 3x - 4 = 0

••••