Question

If one of the zeroes of the quadratic polynomial (α − 1) x² + αx + 1 is −3, then the value of α is ______.

Options

• `−2/3`

• `2/3`

• `4/3`

• `3/4`

Answer 1

If one of the zeroes of the quadratic polynomial (α − 1) x² + αx + 1 is −3, then the value of α is `bbunderline(4/3)`.

Explanation:

(α − 1) x² + αx + 1

If −3 is a zero, then substituting x = −3 into the polynomial should yield 0:

(α − 1) (−3) 2 + α (−3) + 1 = 0

Substitute x = −3 into the polynomial:

(α − 1) (9) + α (−3) + 1 = 0

9(α − 1) −3α + 1 = 0

Expand 9(α − 1):

9α − 9 − 3α + 1 = 0

(9α − 3α) + (−9 + 1) = 0

6α − 8 = 0

Add 8 to both sides:

6α = 8

`alpha = 8/6 = 4/3`