If α and β are the zeros of the polynomial 2x² + x - 6, then form a quadratic equation whose zeros are 2α and 2β.

We know that, for a quadratic equation ax² + box + c

Sum of zeroes

Product of zeroes

Given equation = 2x² + x - 6 and zeroes are α and β

Therefore,

….[1] and

….[2]

Now, any quadratic equation having α and β as zeroes will have the form

p(x) = x² - (α + β)x + αβ

⇒ equation having α and β as zeroes will have the form

p(x) = x² - (2α + 2β)x + (2α)(2β)

⇒ p(x) = x² - 2(α + β)x + 4αβ

From [1] and [2]

Hence required equation is x² + x - 12.