Question

The sum and product of the zeroes of a quadratic polynomial are 19/3 and 2, respectively. If the coefficient of x2 is 6, find the quadratic polynomial.

Answer 1

$\alpha + \beta = \frac{19}{3}$

$\alpha \beta = 2$

Quadratic Polynomial =

${x}^{2} - ( \alpha + \beta )x + \alpha \beta$

${x}^{2} - \frac{19x}{3} + 2 = 0$

$3 {x}^{2} - 19x + 6 = 0$

Since the coefficient of x square needs to be 6, we will multiply the whole polynomial by 2.

$6 {x}^{2} - 38x + 12 = 0$

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