Answers

2015-09-19T06:36:46+05:30
I know only the first solution,
Solution: Given polynomial = 9x² - 1
⇒9x² - 3x + 3x - 1
⇒3x(3x - 1) + 1(3x - 1)
⇒(3x - 1) (3x + 1)
To obtain the zeroes of the polynomial
⇒(3x - 1)(3x + 1) = 0
⇒3x - 1 = 0   or   3x + 1 = 0
⇒3x = 1        or   3x = -1
⇒x = 1/3       or   x = -1/3
∴The zeroes are α = 1/3 and β= -1/3.
for the polynomial given to us, a = 9 , b = 0 and c= -1
Verifying the relation between the zeroes and the coefficients of the given polynomial.
1)  α + β = -b/a
⇒1/3 + [-1/3] = -0/9
⇒1/3 - 1/3 =0
⇒0 = 0.
2)  αβ = c/a 
⇒1/3[-1/3 = -1/9
⇒-1/9 = -1/9
Hence verified.
0