Question

Pls help!!

Question:

The polynomial f (x) = ax2 + bx + c has zeros 4 and 5, and f (−1) = 60. Evaluate a, b and c.

Answer 1

a = 2, b = -18, c = 40

Explanation:

`Given:\ Polynomial\ f(x)=ax^2+bx+c\ has\ zoroes\ 4\ aud\ 5`

`and\ f(-1)=60`

`Tofind:\ a,\ b,\ c`

`Solution:\ As\ 4\ and\ 5\ are\ zeroes\ so\ f(4)=f(5)=0`

`f(4)=a(4)^2+b(4)+c=0\Rightarrow16a+4b+c=0-(1)`

`f(5)=a(5)^2+b(5)+c=0\Rightarrow25a+5b+c=0`

`f(-1)=a(-1)^2+b(-1)+c=60\Rightarrowa-b+c=60-(3)`

`subtracting\ (1)\ from\ (2)`

`25a+5b+c-(16a+4b+c)=0\Rightarrow9a+b=0\Rightarrowb=-9a`

`subtracting\ (3)\ from(2):`

`25a+5b+c-(a-b+c)=0-60\Rightarrow24a+6b=-60`

`putting\ b=-9a`

`24a+6(-9a)=-60\Rightarrow24a-54a=-60\Rightarrow-30a=-60`

`a=(-60)/(-30)=2`
`\Rightarrow`
`a=2`

`b=-9a=-9*2=-18`

`c=-a+b\\eq60=-2-18+60=-20+60=40`

I hope this helps you

:)