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If x-2 is a factor of x2+ax-6 and x2-9x + b find the value of a and b​

Answer»

Hey there!!

To SOLVE this question, we will be using the zero theorem.

We know that ( x -2 ) is a factor of x² + ax - 6. This means, it leaves a REMAINDER of 0 and when x - 9x + b is divided by ( x - 2 ), it leaves a remainder of 0 too.

We will know take x - 2 = 0 and take x as 2.

Now, all we have to do is SUBSTITUTE the value of 'x' in both equations and find the value of a and b.

First, let's find for a :

x² + ax - 6 ; we know that x is 2

... (2)² + a(2) - 6 = 0

... 4 + 2a - 6 = 0

... -2 + 2a = 0

... 2a = 2

... a = 1

Now, let's solve for b:

x² - 9x + b ; We know that x is 2.

... (2)² - 9(2) + b = 0

... 4 - 18 + b = 0

... -14 + b = 0

... b = 14

We now know the values of a and b. a = 1 , b = 14



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