Find the zeroes of the following quadratic polynomial and verify the r

1.	Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.3x2 – x – 4
Answer» Given polynomial is 3x² – x – 4 we have, 3x² – x – 4 = 3x² + 3x – 4x – 4 = 3x(x + 1) – 4(x + 1) = (x + 1) (3x – 4) The value of 3x² – x – 4 is 0 when the value of (x + 1) (3x – 4) is 0. i.e., when x + 1 = 0 or 3x – 4 = 0 i.e., when x = -1 or x = 4/3 ∴ The zeroes of 3x² – x – 4 are -1 and 4/3 Therefore, sum of the zeroes = -1 + 4/3 = -3 +4 /3 = 1/3 = \(=-\frac{Coefficient\,of\,x}{Coefficient\,of\,x^2}=\frac{-(-1)}{3}=\frac{1}{3}\) And product of the zeroes -1 × 4/3 = -4/3 \(=\frac{Constant\,term}{Coefficient\,of\,x^2}=\frac{-4}{3}\)

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.3x2 – x – 4

Answer»

Given polynomial is 3x² – x – 4

we have, 3x² – x – 4 = 3x² + 3x – 4x – 4

= 3x(x + 1) – 4(x + 1) = (x + 1) (3x – 4)

The value of 3x² – x – 4 is 0 when the value of (x + 1) (3x – 4) is 0.

i.e., when x + 1 = 0 or 3x – 4 = 0

i.e., when x = -1 or x = 4/3

∴ The zeroes of 3x² – x – 4 are -1 and 4/3

Therefore, sum of the zeroes = -1 + 4/3 = -3 +4 /3 = 1/3

= \(=-\frac{Coefficient\,of\,x}{Coefficient\,of\,x^2}=\frac{-(-1)}{3}=\frac{1}{3}\)

And product of the zeroes -1 × 4/3 = -4/3

\(=\frac{Constant\,term}{Coefficient\,of\,x^2}=\frac{-4}{3}\)