Question

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

3x² – x – 4

Answer 1

3x² – x – 4

= 3x² – 4x + 3x – 4

= x(3x – 4) + 1(3x - 4)

= (3x – 4)(x + 1)

For p(x) = 0 we have, 

Either (x + 1) = 0

x = –1

or 3x – 4 = 0

`x = 4/3`

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

Now,

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

= `(-1) + 4/3`

= `(-(-1))/3`

= `1/3 = 1/3`

and product of zeroes `"Constant term"/("Coefficient of " x^2)`

`(-1)xx 4/3 = (-4)/3`

= `(-4)/3 = (-4)/3`

Thus, the relationship between the zeroes and coefficients in the polynomial 3x² – x – 4 is verified.