Question

the quadratic equation whose roots are -2,-3 are​

Answer 1

Step-by-step explanation:

$\alpha + \beta = - 2 \: \: and \: \: \alpha \times \beta = - 3$

so the quadratic equations will be in for of

${x}^{2} + ( \alpha + \beta )x + ( \alpha \times \beta ) = 0$

as we know

$\alpha + \beta = \frac{ - b}{a} \: and \: \alpha \times \beta = \frac{c}{a} \\ a {x}^{2} + bx + c = 0$

so quadratic equation is

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

it is the correct answer

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Answer 2

Answer:

x² + 5x + 6

Step-by-step explanation:

Given :- roots = -2 and -3

Sum of roots ( alpha + beta) = -2 + (-3) = -2-3 = -5

Product of roots ( alpha×Beta) = -2 × -3 = 6

Required quadratic equation

= x² - (alpha + beta)x + alpha×Beta = 0

= x² - (-5)x + 6 = 0

= x² + 5x + 6 = 0