Factorise : -2x² - 14x + 9
Mathématiques
gaellehue94200
Question
Factorise :
-2x² - 14x + 9
-2x² - 14x + 9
1 Réponse
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1. Réponse Anonyme
Bonjour Gaellehue94200
[tex]-2x^2 - 14x + 9=-2(x^2 +7x -\dfrac{9}{2})\\\\-2x^2 - 14x + 9=-2[(x^2 +7x+(\dfrac{7}{2})^2)-(\dfrac{7}{2})^2 -\dfrac{9}{2}]\\\\-2x^2 - 14x + 9=-2[(x+\dfrac{7}{2})^2-\dfrac{49}{4} -\dfrac{9}{2}]\\\\-2x^2 - 14x + 9=-2[(x+\dfrac{7}{2})^2-\dfrac{49}{4} -\dfrac{18}{4}][/tex]
[tex]\\\\-2x^2 - 14x + 9=-2[(x+\dfrac{7}{2})^2-\dfrac{67}{4}]\\\\-2x^2 - 14x + 9=-2[(x+\dfrac{7}{2})^2-(\dfrac{\sqrt{67}}{2})^2]\\\\-2x^2 - 14x + 9=-2[(x+\dfrac{7}{2})-\dfrac{\sqrt{67}}{2}][(x+\dfrac{7}{2})+\dfrac{\sqrt{67}}{2}]\\\\\\\boxed{-2x^2 - 14x + 9=-2(x+\dfrac{7}{2}-\dfrac{\sqrt{67}}{2})(x+\dfrac{7}{2}+\dfrac{\sqrt{67}}{2})}\\\\\\\boxed{-2x^2 - 14x + 9=-2(x+\dfrac{7-\sqrt{67}}{2})(x+\dfrac{7+\sqrt{67}}{2})}[/tex]