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Quadratic Equations · Class 10 · CBSE Mathematics

Find the roots of the quadratic equation sqrt{2}x^2 + 7x + 5sqrt{2} = 0.

Practice question from Quadratic Equations (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-74126A

Find the roots of the quadratic equation 2x2+7x+52=0\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0.

  1. A.−2,−52-\sqrt{2}, -\frac{5}{\sqrt{2}}Correct answer
  2. B.2,52\sqrt{2}, \frac{5}{\sqrt{2}}
  3. C.−2,52-\sqrt{2}, \frac{5}{\sqrt{2}}
  4. D.2,−52\sqrt{2}, -\frac{5}{\sqrt{2}}

Solution

Using splitting the middle term: 2x2+5x+2x+52=0\sqrt{2}x^2 + 5x + 2x + 5\sqrt{2} = 0, which gives x(2x+5)+2(2x+5)=0x(\sqrt{2}x + 5) + \sqrt{2}(\sqrt{2}x + 5) = 0. This implies (2x+5)(x+2)=0(\sqrt{2}x + 5)(x + \sqrt{2}) = 0. Thus, x=−2x = -\sqrt{2} or x=−52x = -\frac{5}{\sqrt{2}}.

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