Question

a polynomial equation which zeros 5 and -3 find the equation​

Answer 1

Answer:finding the polynomial equation where f(0)=f(5)=0 and f(2)=-12.

:

Using the form y = ax^2 + bx + c; (a 2nd degree equation)

:

When the y intercept is 0, then c = 0, therefor the equation becomes just:

y = ax^2 + bx

:

f(5)=0 then x=5; y=0

5^2a + 5b = 0

25a + 5b = 0

:

f(2)=-12: x=2; y=-12

2^2a + 2b = -12

4a + 2b = -12

:

Use elimination, multiply the 1st equation by 2, the 2nd equation by 5:

50a + 10b = 0

20a + 10b = -60

-------------------subtraction eliminates b, find a

30a = +60

a = 2

:

Find b using the 1st equation:

25(2) + 5b = 0

50 + 5b = 0

5b = -50

b = -10

:

the equation: f(x) = 2x^2 - 10x

Answer 2

Answer:

Step-by-step explanation:

the equation will be written as

x^2+(sum of roots)x+product of roots=0

sum = 5+(-3)= 2

product = 5*-3= - 15

so the equation is

x^2+2x-15=0