if the zero of polynomial x square minus 3 X square + X + 1 are (a +b), a, (a+b) find the value of a and b
Answers
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u r question is incorrect it will be x cube minus 3 x square
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GIVEN :
The zeros of polynomial are (a -b), a, (a+b)
TO FIND :
The values of a and b
SOLUTION :
Given polynomial is
Equate the polynomial to zero to find the zeros
By using the Synthetic Division Method
1_| 1 -3 1 1
0 1 -2 -1
______________
1 -2 -1 0
∴ x-1 is a factor
x-1=0
∴ x=1 is a zero
Now we have the quadratic equation
The formula for the quadratic equation for x is :
Comparing the coefficients in quadratic equation with the general quadratic equation we get a=1 , b=-2 and c=-1
Now substitute the values in the formula we have
∴ and are the zeros
∴ the zeros are 1 , and
Comparing with the given zeros a, a+b and a-b with the zeros
1 , and we get
Hence we get a=1 and
∴ the value of a is 1 and b is