Question

find the zeros of the polynomial f(x)=2xcube -9x square +x +12 . please tell how to solve​

Answer 1

Answer:

Given f(x)=2x

2

+2ax+5x+10

g(x)=x+a

x+a=0

x=−a

f(−a)=2(−a)

2

+2a(−a)+5(−a)+10

⇒+2a

2

−2a

2

−5a+10=0

⇒5a=10

⇒a=

5

10

∴a=2

Answer 2

$\huge\mathfrak\pink{Question}$

FIND THE ZERO  THE POLYNOMIAL:-

$P(x)=2x^3-9x^2+x+12$

EXPLANATION:-

$p(-1)=2(-1)^3-9(1)^2+(-1)+12\\p(-1)=0$

so -1 is zero of the polynomial of and x+1 is factor of the given polynomial

NOW LET'S DIVIDE $P(x)=2x^3-9x^2+x+12$ BY x+1 to get other factor  

SO WE GET quotient  AS $2x^2-11x+12$  (see 1 attachment for process division)

NOW,

WE GET FACTORS AS (x+1)(2x^2-11x+12)

on solving we get that factors are:-

(x+1)(2x-3)(x-4)

and zeroes of the given polynomial is :-

-1,3/2 & 4

hope it helps  u

$\huge\red{D}\pink{E}\orange{V}\green{A}\blue{N}\gray{S}\red{H}\orange{U}$