The roots of the fallowing functions are the Sequences of arithmetic progressiyon f(x)=x^5 −20x^4 +ax^3 +bx^2 +cx+24 f(8)=?


Question and Answers Forum

All Questions Topic List
Arithmetic Questions
Previous in All Question Next in All Question
Previous in Arithmetic Next in Arithmetic
Question Number 50445 by ANTARES VY last updated on 16/Dec/18

$The roots of the fallowing$ $functions are the Sequences of$ $arithmetic progressiyon$ $f (x) = x^{5} - 20 x^{4} + {ax}^{3} + {bx}^{2} + cx + 24$ $f (8) = ?$
Commented by tanmay.chaudhury50@gmail.com last updated on 16/Dec/18

$p l s c h e c k t h e q u e s t i o n . .$ $i f f (x) = 0$ $v a l u e o f x i s i n t e r m s o f a, b, c$ $s o$ $f (8) = 8^{5} - 20 \times 8^{4} + a \times 8^{3} + b \times 8^{2} + c \times 8 + 24$
	Answered by ajfour last updated on 16/Dec/18

	$l e t r o o t s b e$ $x_{i} = p - 2 q, p - q, p, p + q, p + 2 q$ $\Rightarrow Σ x_{i} = 5 p = 20 \Rightarrow p = 4$ $Π x_{i} = p (p^{2} - q^{2}) (p^{2} - 4 q^{2}) = - 24$ $l e t q^{2} = s$ $\Rightarrow (16 - s) (16 - 4 s) + 6 = 0$ $4 s^{2} - 80 s + 262 = 0$ $o r 2 s^{2} - 40 s + 131 = 0$ $s = q^{2} = 10 \pm \frac{\sqrt{138}}{2}$ $(n o t a c o n v i n i e n t v a l u e . .)$ $a = Σ x_{1} x_{2}$ $b = - Σ x_{1} x_{2} x_{3}$ $c = Σ x_{1} x_{2} x_{3} x_{4}$ $f (8) = 8^{5} - 20 {(8)}^{4} + a {(8)}^{3} + b {(8)}^{2}$ $+ 8 c + 24$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum