Find a quadratic function

Question

Find a quadratic function whose zeros are twice the zeros of y=6x^2+13x-5.

Can you add how to do it.(solution)

Answer 1

y=6x^2+13x-5

 

Given an equation of form  y = ax²+bx +c

The zeroes of this are derived from quadratic equation

x = [-b ±√(b² - 4ac)]/2a

 

To find zeroes that are double this, we would multiply this by 2 giving

a polynomial with zeroes at:

 

x = [-b ±√(b² - 4ac)]/a   with  a=6, b=13, c = -5

 

x = [-13 ±√(13²-4(6)(-5))]/6

 

x = [-13 ±√289]/6

 

x = (-13 ± 17)/6

 

x = (-13+17)/6 = 4/6 = 2/3

OR

x = (-13-17)/6 = -30/6 = -5

 

The zeroes we are looking for are x = 2/3 and x=-5

 

If 2/3 is a zero then (x-2/3) is a factor

If -5 is a zero then (x+5) is a factor

 

Your polynomial is:  y = (x-2/3)(x+5)

This can be multiplied out using FOIL giving:

y = x² + (13/3)x - 10/3