If x²– 3x + 2 divides x²–2x-x+2 exactly, then find the value
of ‘a’ and ‘b
Answers
Answer:
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Step-by-step explanation:
find the roots of
{x}^{2} - 3x + 2x
2
−3x+2
then place these values in the second polynomial,you will get two equation,solve them for calculating a and b.
\begin{gathered} {x}^{2} - 3x + 2 = 0 \\ {x}^{2} - 2x - x + 2 = 0 \\ x(x - 2) - 1(x - 2) = 0 \\ (x - 2)(x - 1) = 0 \\ x - 2 = 0 \\ x = 2 \\ x - 1 = 0 \\ x = 1 \end{gathered}
x
2
−3x+2=0
x
2
−2x−x+2=0
x(x−2)−1(x−2)=0
(x−2)(x−1)=0
x−2=0
x=2
x−1=0
x=1
put x = 2
\begin{gathered} {x}^{3} - 6 {x}^{2} + ax + b = 0 \\ 8 - 6(4) + 2a + b = 0 \\ 8 - 24 + 2a + b = 0 \\ 2a + b = 16\end{gathered}
x
3
−6x
2
+ax+b=0
8−6(4)+2a+b=0
8−24+2a+b=0
2a+b=16
put x= 1
\begin{gathered} {x}^{3} - 6 {x}^{2} + ax + b = 0 \\ 1 - 6 + a + b = 0 \\ a + b = 5\end{gathered}
x
3
−6x
2
+ax+b=0
1−6+a+b=0
a+b=5
subtract both equations
\begin{gathered}2a - a \: = 16 - 5 \\ a = 11\end{gathered}
2a−a=16−5
a=11
\begin{gathered}a + b = 5 \\ 11 + b = 5 \\ b = 5 - 11 \\ b = - 6\end{gathered}
a+b=5
11+b=5
b=5−11
b=−6