Question

The sum and product of zeroes of a quadratic polynomial p(x) are `(-1)/3 and 2` respectively. The polynomial p(x) is ______.

पर्याय

• 3x² − x + 6

• `x^2 + 1/3 x - 2`

• 3x² − x + 2

• −3x² − x − 6

Answer 1

The sum and product of zeroes of a quadratic polynomial p(x) are `(-1)/3 and 2` respectively. The polynomial p(x) is 3x² + x + 6.

Explanation:

Let sum of quadratic polynomial is α + β = `(-1)/3`

Product of the quadratic polynomial is (αβ) = 2

The required polynomial g⁡(x) is given by

p⁡(x) = k[x² − Sx + P]

p⁡(x) = k[x² − (α + β) x + (αβ)]

p(x) = `k[x^2 - (-1/3)x + 2]`

= `k[x^2 + 1/3  x + 2]`

To eliminate the fraction, we can choose k = 3

p(x) = `3(x^2 + 1/3  x + 2)`

= 3x² + 3x + 6

Wait, let’s re-examine the options and the signs. If we take k = −3.

p(x) = `-3(x^2 + 1/3  x + 2)`

= −3x² − x − 6