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2̊ grau com uma incógnita no conjunto dos números reais. a) \( x^{2}+2 x-15=0 \)

Ask by Black Sullivan. in Brazil
Nov 28,2024

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Answer

As soluções são \(x=-5\) e \(x=3\).

Solution

Solve the equation \( x^{2}+2x-15=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(x^{2}+2x-15=0\) - step1: Factor the expression: \(\left(x-3\right)\left(x+5\right)=0\) - step2: Separate into possible cases: \(\begin{align}&x-3=0\\&x+5=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=3\\&x=-5\end{align}\) - step4: Rewrite: \(x_{1}=-5,x_{2}=3\) A equação \(x^{2}+2x-15=0\) tem duas soluções reais: \(x=-5\) e \(x=3\).

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Para resolver a equação quadrática \( x^{2}+2x-15=0 \), podemos utilizar a fórmula de Bhaskara. Os coeficientes são \( a = 1 \), \( b = 2 \) e \( c = -15 \). Calculamos o discriminante: \( \Delta = b^{2} - 4ac = 2^{2} - 4 \cdot 1 \cdot (-15) = 4 + 60 = 64 \). Como o discriminante é positivo, a equação possui duas raízes reais e distintas. Aplicando a fórmula de Bhaskara, encontraremos as raízes: \( x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{-2 \pm 8}{2} \). Isso nos dá as soluções \( x = 3 \) e \( x = -5 \). Agora é só escolher a que combina mais com teu estilo! 😉

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