If-f-x-ax-2-5x-3-and-g-x-3x-3-intersection-at-points-1-h-and-3-t-Find-

Question Number 194809 by dimentri last updated on 16/Jul/23

I f f (x) = {a x}^{2} - 5 x + 3 a n d

g (x) = 3 x - 3 i n t e r s e c t i o n a t

p o i n t s (1, h) a n d (3, t) .

F i n d \underset{―}{}

Answered by horsebrand11 last updated on 16/Jul/23

f (x) = a (x - 1) (x - 3) + g (x)

{ax}^{2} - 5 x + 3 = {ax}^{2} - 4 ax + 3 a + 3 x - 3

{ax}^{2} - 5 x + 3 = {ax}^{2} - (4 a - 3) x + 3 (a - 1)

{\begin{cases} 5 = 4 a - 3 \\ 1 = a - 1 \end{cases} \Rightarrow \begin{matrix} a = 2 \end{matrix}

∴ f (x) = {2 x}^{2} - 5 x + 3

f (2) - f (- 2) = 1 - 21 = \begin{matrix} - 20 \end{matrix}

Commented by dimentri last updated on 16/Jul/23

\underset{―}{\underset{⏟}{x}}

Answered by Rasheed.Sindhi last updated on 16/Jul/23

f (1) = g (1) = h

a {(1)}^{2} - 5 (1) + 3 = 3 (1) - 3 = h

a - 2 = 0

a = 2

f (x) = 2 x^{2} - 5 x + 3

f (2) - f (- 2)

= {2 {(2)}^{2} - 5 (2) + 3} - {2 {(- 2)}^{2} - 5 (- 2) + 3}

= 1 - 21 = - 20

∙ “ (3, t) i s i n t e r s e c t i o n {p o i n t}^{″} i s

u n n e c e s s a r y . O n e c o m m o n p o i n t

i s s u f f i c i e n t h e r e .

Commented by dimentri last updated on 16/Jul/23