Question

If the zeroes of the polynomial f(x) = x³ – 3x² + x + 1 are (a – b), a and (a + b), find the values of a and b.

If the zeros of the polynomial f(x) = x³ – 3x² + x + 1 are (a – b), a and (a + b), find a and b.

Answer 1

By using the relationship between the zeroes of the quadratic polynomial.

We have,

Sum of zeroes = `(-("Coefficient of"  x^2))/("Coefficient of"  x^3)` 

∴ a – b + a + a + b = `(-(-3))/1` 

⇒ 3a = 3 

⇒ a = 1 

Now, Product of zeroes = `(-"(Constant term")/("Coefficient of"  x^3)` 

∴ (a – b) (a) (a + b) = `(-1)/1` 

⇒ (1 – b) (1) (1 + b) = –1   ...[∵ a = 1] 

⇒ 1 – b² = –1 

⇒ b² = 2 

⇒ b = `+-sqrt2`