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Questions
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.
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Solution
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`
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