if x-2 is a factor of x2+ax-6 and x2-9x + b find the value of a and b
Answers
Answered by
11
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
Similar questions