Question

Simplify and find their values if x=2a =-1 10a-2x+5​

Answer 1

Step-by-step explanation:

Answer:

The value of a is termed to be 2.

Solution:

Given that

2 x ^ { 2 } + 2 a x + 5 x + 102x2+2ax+5x+10

Divide the 2 x ^ { 2 } + 2 a x + 5 x + 102x2+2ax+5x+10 by x+ax+a

By using the division method, we get the remainder as 10-5a

\begin{gathered}\begin{array} { l } { 10 - 5 a = 0 } \\\\ { 5 a = 10 } \\\\ { \therefore a = 2 } \end{array}\end{gathered}10−5a=05a=10∴a=2

Another method:

We can also find the value of a by this method,  

Let x+a=0x+a=0

x=-ax=−a

Substitute the value of x in the given equation,

\begin{gathered}\begin{array} { c } { 2 \mathrm { x } ^ { 2 } + 2 \mathrm { ax } + 5 \mathrm { x } + 10 = 0 } \\\\ { 2 ( - \mathrm { a } ) ^ { 2 } + 2 \mathrm { a } ( - \mathrm { a } ) + 5 ( - \mathrm { a } ) + 10 = 0 } \\\\ { 2 a ^ { 2 } - 2 a ^ { 2 } - 5 a + 10 = 0 } \\\\ { - 5 a + 10 = 0 } \end{array}\end{gathered}2x2+2ax+5x+10=02(−a)2+2a(−a)+5(−a)+10=02a2−2a2−5a+10=0−5a+10=0

\begin{gathered}\begin{array} { c } { - 5 a = - 10 } \\\\ { 5 a = 10 } \\\\ { a = \frac { 10 } { 5 } = 2 } \end{array}\end{gathered}−5a=−105a=10a=510=2

Thus, we can find the value of a=2 in this method also.