Question

Find the zeroes of the quadratic polynomial 6x² – 3 – 7x and verify the relationship between the zeroes and the coefficients.

Answer 1

6x² – 7x – 3 = 0

⇒ 6x² – 9x + 2x – 3 = 0

⇒ 3x(2x – 3) + 1(2x – 3) = 0

⇒ (2x – 3)(3x + 1) = 0

⇒ 2x – 3 = 0 and 3x + 1 = 0

⇒ 2x = 3 and 3x = −1

⇒ x = `3/2` and x = `(-1)/3`

Let considered x = `3/2` be α and x = `(-1)/3` be β.

α + β = `3/2 + ((-1)/3) = (9 - 2)/6 = 7/6`

`(-"b")/"a" = (-(-7))/6 = 7/6`

⇒ α + β = `(-"b")/"a"`

αβ = `3/2 xx (-1)/3 = (-1)/2`

`"c"/"a" = (-3)/6 = (-1)/2`

αβ = `"c"/"a"`