Question

if f(x)=xcube+xsquar+ax+b is divisible by xsquar-x find the value of a and b.

Answer 1

Hey!

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f (x) = x^3 + x^2 + ax + b

According to Question, x^2 - x is divisible by f (x)

x^2 - x = 0

x ( x - 1) = 0

Values of x = 0 and 1

Let's keep the values -:



• f ( 0 ) = 0 + 0 + 0 + b = 0

0 + b = 0

b = 0

• f ( 1 ) = 1 + 1 + a + 0 = 0

2 + a = 0

a = - 2

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Hope it helps...!!!

Answer 2

Hello friend

Your answer is given below :::::=>

$given \: that \: \\ f(x) = {x}^{3} + {x + ax + b}^{2} \\ and \: {x}^{2} - x = 0 \: (given)$
♠️=> x (x-1) = 0

♠️=> x=0 and x = 1

♠️If x = 0, then

F(0) => (0)^3 + (0)^2 + a(0) + b

♠️=> b= 0

♠️If x=1

Then,

F(1 ) => (1 )^3 (1)^2 a(1) 0 = 0

♠️=> 1 + 1 + a = 0

♠️=> a = - 2

So the values of

♠️a = -2

♠️ b = 0
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Have a great day.......

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