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2. Polynomials
hard
$2x + 3$ એ $2 x^{3}+21 x^{2}+67 x+60$ નો અવયવ છે કે નહીં તે ચકાસો.
Option A
Option B
Option C
Option D
Solution
$2 x+3$ નું શૂન્ય $\left(-\frac{3}{2}\right)$ છે.
$p(x)=2 x^{3}+21 x^{2}+67 x+60$
$\therefore p\left(-\frac{3}{2}\right)=2\left(-\frac{3}{2}\right)^{3}+21\left(-\frac{3}{2}\right)^{2}+67\left(-\frac{3}{2}\right)+60$
$=2\left(-\frac{27}{8}\right)+21\left(\frac{9}{4}\right)-\frac{201}{2}+60$
$=-\frac{27}{4}+\frac{189}{4}-\frac{201}{2}+60$
$=\frac{-27+189-402+240}{4}$
$=\frac{-429+429}{4}=\frac{0}{4}$
$\therefore p\left(-\frac{3}{2}\right)=0$
તેથી અવયવ પ્રમેય મુજબ $2 x+3$ એ $2 x^{3}+21 x^{2}+67 x+60$ નો અવયવ છે.
Standard 9
Mathematics