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

Answer:

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

Step-by-step explanation:

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

$and\ f(-1)=60$

$Tofind:\ a,\ b,\ c$

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

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

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

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

$subtracting\ (1)\ from\ (2)$

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

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

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

$putting\ b=-9a$

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

$a=\frac{-60}{-30}=2$ $\Rightarrow$ $a=2$

$b=-9a=-9\times2=-18$

$c=-a+b\neq60=-2-18+60=-20+60=40$

I hope this helps you

:)