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Mathematics · Quadratic Equations · NCERT Examples

Example 2

A complete, independently verified solution for NCERT Example 2.

Mathematics · Chapter 4 · NCERT Examples

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NCERT Example

Example 2

quadratic equations · standard form

Check whether each equation is quadratic.

  1. (x−2)2+1=2x−3(x-2)^2+1=2x-3
  2. x(x+1)+8=(x+2)(x−2)x(x+1)+8=(x+2)(x-2)
  3. x(2x+3)=x2+1x(2x+3)=x^2+1
  4. (x+2)3=x3−4(x+2)^3=x^3-4

Solution

  1. x2−4x+5=2x−3⇒x2−6x+8=0x^2-4x+5=2x-3\Rightarrow x^2-6x+8=0

    Quadratic.

  2. x2+x+8=x2−4⇒x+12=0x^2+x+8=x^2-4\Rightarrow x+12=0

    Not quadratic.

  3. 2x2+3x=x2+1⇒x2+3x−1=02x^2+3x=x^2+1\Rightarrow x^2+3x-1=0

    Quadratic.

  4. x3+6x2+12x+8=x3−4⇒x2+2x+2=0x^3+6x^2+12x+8=x^3-4\Rightarrow x^2+2x+2=0

    Quadratic after dividing by 6.