Question

form a quadratic equation whose roots are -4 and 5/3​

Answer 1

$\large\underline{\underline{\frak{\maltese\:\: \red{Given : }}}}$

1st Root (α) = -4

2nd Root (β) = $\frac {5}{3}$

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$\large\underline{\underline{\frak{\maltese\:\: \red{Knowledge \: Required\: :}}}}$

» General form of Quadratic Equation = x ² - (Sum of its roots) + Product of its roots

» General form of Quadratic Equation = x² - (α + β)x + αβ

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$\large\underline{\underline{\frak{\maltese\:\: \red{Solution \: : }}}}$

$\odot \: \alpha \: + \: \beta = - 4 \: + \: \frac{5}{3}$

$\leadsto \: \alpha \: + \: \beta = \frac{-12 \: + \: 5}{3}$

$\leadsto \: \boxed{\bold{\underline{\alpha \: + \: \beta = \frac{-7}{3}}}}$

$\odot \: \alpha \: \times \: \beta = -4 \: \times \: \frac {5}{3}$

$\leadsto \: \boxed{\bold{\underline{\alpha \beta = \frac{-20}{3}}}}$

Quadratic Equation = x² - (α + β)x + αβ

Quadratic Equation = x² - $\bold{(\frac{-7}{3})}$x - $\bold{\frac{20}{3}}$

Quadratic Equation = x² + $\bold{\frac{7}{3}}$x - $\bold{\frac{20}{3}}$

$\boxed{\bold{ \underline{\therefore \: Quadratic \: Equation = x^2 \: + \: \frac{7}{3}x \: - \:\frac{20}{3}}}}$