Răspuns:
[tex]\boldsymbol{ a) \ \red{(x + 2)(x + 5)}}[/tex]
[tex]\boldsymbol{b) \ \red{3\bigg(x - \dfrac{4}{3} \bigg)\bigg(x - 1\bigg)}}[/tex]
Explicație pas cu pas:
a) x² + 7x + 10 = 0
a = 1, b = 7, c = 10
[tex]\boldsymbol{\Delta = b^{2} - 4ac} = 7^{2} - 4 \cdot 1 \cdot 10 = 49 - 40 = 9[/tex]
[tex]\boldsymbol{ x_{1,2} = \dfrac{-b \pm \sqrt{\Delta} }{2a} } = \dfrac{-7 \pm \sqrt{9} }{2 \cdot 1} = \dfrac{-7 \pm 3}{2}[/tex]
[tex]x_{1} = \dfrac{-7 - 3}{2} = -\dfrac{10}{2} \Rightarrow \boldsymbol{ x_{1} = - 5}[/tex]
[tex]x_{2} = \dfrac{-7 + 3}{2} = -\dfrac{4}{2} \Rightarrow \boldsymbol{ x_{2} = - 2}[/tex]
⇒ x² + 7x + 10 = (x + 2)(x + 5)
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b) 3x² - 7x + 4 = 0
a = 3, b = -7, c = 4
[tex]\boldsymbol{\Delta = b^{2} - 4ac} = (-7)^{2} - 4 \cdot 3 \cdot 4 = 49 - 48 = 1[/tex]
[tex]\boldsymbol{ x_{1,2} = \dfrac{-b \pm \sqrt{\Delta} }{2a} } = \dfrac{-(-7) \pm \sqrt{1} }{2 \cdot 3} = \dfrac{7 \pm 1}{6}[/tex]
[tex]x_{1} = \dfrac{7 - 1}{6} = \dfrac{6}{6} \Rightarrow \boldsymbol{ x_{1} = 1}[/tex]
[tex]x_{2} = \dfrac{7 + 1}{6} = \dfrac{8}{6} \Rightarrow \boldsymbol{ x_{2} = \dfrac{4}{3}}[/tex]
⇒ 3x² - 7x + 4 = (3x - 4)(x - 1)
