Question

A quadratic polynomial, whose zeroes are –3 and 4, is ______.

Options

• `x^2 - x + 12`

• `x^2 + x + 12`

• `x^2/2 - x/2 - 6`

• `2x^2 + 2x - 24`

Answer 1

A quadratic polynomial, whose zeroes are –3 and 4, is `x^2/2 - x/2 - 6`.

Explanation:

Sum of zeroes, α + β= – 3 + 4 = 1

Product of Zeroes, αβ = – 3 × 4 = –12

Therefore, the quadratic polynomial becomes,

x² – (sum of zeroes)x+(product of zeroes)

= x² – (α + β)x + (αβ)

= x² – (1)x + (–12)

= x² – x – 12

Divide by 2, we get

= `x^2/2 - x/2 -12/2`

= `x^2/2 - x/2 - 6`