Question

Please answer it...
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Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow g(x)=x+1$

$\sf\dashrightarrow p(x)=2x^3+ax^2+2bx+1\:and\: 2a-3b=4$

$\large\underline\bold{TO\:FIND,}$

$\sf\large\dashrightarrow the\:value\:of\:'a'\:and'b'.$

NOTE:–

$\sf {\boxed{\bf{\:\: to\:find\:zeroes\:of\:the\:polynomial\:we\:need\:p(x)=0}}}$

$\large\underline\bold{SOLUTION,}$

TAKING g(x)=x+1

$\sf\implies x+1=0$

$\sf\implies x=-1$

✯PUTTING THE VALUE OF X IN P(x),

we get,

$\sf\therefore 2x^3+ax^2+2bx+1=0$

$\sf\implies 2(-1)^3+a(-1)^2+2b(-1)+1=0$

$\sf\implies (-2)+a-2b+1=0$

$\sf\implies a-2b-1=0$

$\sf\implies a-2b=1$

$\sf\implies a=1+2b\:---equation^1$

NOW,

taking ,

$\sf\dashrightarrow 2a-3b=4\:----[taking\:as\:equation\:2_{nd}]$

PUTTING THE VALUES OF EQUATION 1 IN EQUATION 2,

WE GET,

$\sf\therefore a=1+2b$

$\sf\implies 2a-3b=4$

$\sf\implies 2(1+2b)-3b=4$

$\sf\implies 2+4b-3b=4$

$\sf\implies 2+b=4$

$\sf\implies b=2$

$\large{\boxed{\bf{\star\:\: b=2\:\: \star }}}$

PUTTING THE VALUE OF 'b' in equation 1

WE GET,

$\sf\therefore a=1+2b$

$\sf\therefore b=2$

$\sf\implies a=1+2 \times (2)$

$\sf\implies a=1+4$

$\sf\implies a=5$

$\large{\boxed{\bf{\star\:\: a=5\:\: \star }}}$

VERIFICATION,

$\sf\therefore a=5$

$\sf\therefore b=2$

$\sf\therefore x=-1$

$\sf\therefore 2x^3+ax^2+2bx+1=0$

$\sf\implies 2(-1)^3+(5)(-1)^2+(2)(-1)+1=0$

$\sf\implies (-2)+5+(-4)+1=0$

$\sf\implies (-1)+1=0$

$\sf\implies 0=0$

$\sf\therefore L.H.S=R.H.S$

$\sf\therefore 2a-3b=4$

$\sf\implies 2(5)-3(2)=4$

$\sf\implies 10-6=4$

$\sf\implies 4=4$

$\sf\therefore L.H.S=R.H.S$

$\large\underline\bold{HENCE, VERIFYED.}$

$\large\underline\bold{\therefore \:THE\:VALUE\:OF\:'a' \:IS\:5 \:AND\:VALUE\:OF\:'b'\:IS\:2.}$

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Answer 2

Timing of Physics wallah classes

(I) => inorganic chemistry

(O)=>organic chemistry