Question

Find the zeroes of the quadratic polynomial (3x² – x – 4) and verify the relation between the zeroes and the coefficients.

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

3x² – x – 4

Answer 1

3x² – x – 4 = 0

⇒ 3x² – 4x + 3x – 4 = 0

⇒ x(3x – 4) + 1(3x – 4) = 0

⇒ (3x – 4) (x + 1) = 0

⇒ (3x – 4) or (x + 1) = 0 

⇒ `x = 4/3` or x = –1 

Sum of zeroes = `4/3 + (-1)`

= `1/3`

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

Product of zeroes = `4/3 xx (-1)`

= `(-4)/3`

= `("Constant term") /(("Coefficient of "x^2))`