Question

The roots of a quadratic equation are ⅓ and −2. Determine the equation in x.​

Answer 1

Answer:

Let the roots of quadratic equation be Alpha and Beta.

Then,

Alpha will be 1/3 and Beta will be -2.

Then,

Alpha + Beta is 1/3 + (-2)

= 1/3 - 2

= (1 - 6)/2

= -5/2

Alpha × Beta is 1/3 × -2

= -2/3

Then the required quadratic equation will be

x^2 - (Alpha+Beta)x + Alpha×Beta = 0

= x^2 - (-5/2)x + (-2/3) = 0

= x^2 + 5/2x - 2/3 = 0

Hope it helped...

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Answer 2

Answer:

The required equation is 3x^2 + 5x -2 = 0

Step-by-step explanation:

$(x - \frac{1}{3} )(x - ( - 2)) = 0\\ (x - \frac{1}{3} )(x + 2) = 0\\ {x}^{2} + 2x - \frac{x}{3} - \frac{2}{3} = 0 \\ {x }^{2} + \frac{5x}{3} - \frac{2}{3} = 0 \\ 3 {x}^{2} + 5x - 2 = 0$