Question

If 3 is the remainder obtained on dividing the polynomial (y) = y^2 - ay^2+ 2y - 5 by g(y) = y - 2.
Find the value of a​

Answer 1

✧$\huge \mathcal \red {\underline{\underline{A}}}$ $\huge \mathcal \green {\underline{\underline{N}}}$ $\huge \mathcal \pink {\underline{\underline{S}}}$ $\huge \mathcal \blue {\underline{\underline{W}}}$ $\huge \mathcal \orange {\underline{\underline {E}}}$ $\huge \mathcal \purple {\underline{\underline{R}}}$✧

❥ Given :

→ Remainder = 3

→ $p(y) = y² - ay² + 2y - 5$

→ $g(y) = y - 2$

❥ To find :

The value of a

❥ Solution :

→ $g(y) = y - 2$

→ $y - 2 = 0$

→ $y = 2$

Now, put the value y in p(y), i.e, 2

→ $p(y) = y² - ay² + 2y - 5$

→ $p(2) = 2² - a(2)² + 2(2) - 5$

→ $p(2) = 4 - a(4) + 4 - 5$

→ $p(2) = 4a - 3$

→ $4a - 3 = 0$

→ $4a = 3$

→ $a = \frac {3}{4}$

$\implies$ Hence, the value of a is $\: \frac {3}{4} \:$.

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