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2. Polynomials
medium
$p(x)$ ને $g(x)$ વડે ભાગતાં શેષ પ્રમેયની મદદથી મળતી શેષ શોધો.
$p(x)=4 x^{3}-12 x^{2}+14 x-3, g(x)=2 x-1$
A
$\frac{3}{2}$
B
$\frac{1}{2}$
C
$\frac{-1}{2}$
D
$\frac{-3}{2}$
Solution
We have $g(x)=2 x-1$
$\Rightarrow \quad 2 x-1=0$
$\Rightarrow \quad 2 x-1 \Rightarrow x=\frac{1}{2}$
Remainder $=p\left(\frac{1}{2}\right)$
$=4\left(\frac{1}{2}\right)^{3}-12\left(\frac{1}{2}\right)^{2}+14\left(\frac{1}{2}\right)-3$
$=4\left(\frac{1}{8}\right)-12\left(\frac{1}{4}\right)+7-3$
$=\frac{1}{2}-3+7-6=\frac{1}{2}-2=\frac{-3}{2}$
Standard 9
Mathematics
