Multiple choice

How many of the following are quadratic equation? (i) $(x + 2)^3 = 2x (x^2 - 1)$ (ii) $(x-3)(2x+1)=x(x+5)$ (iii) ${ x }^{ 2 }-3x+2=0$

  1. $0$
  2. $3$
  3. $2$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

(i) (x+2)^3 = x^3 + 6x^2 + 12x + 8. RHS = 2x^3 - 2x. Result: x^3 - 6x^2 - 14x - 8 = 0 (cubic). (ii) 2x^2 - 5x - 3 = x^2 + 5x. Result: x^2 - 10x - 3 = 0 (quadratic). (iii) x^2 - 3x + 2 = 0 (quadratic). Two are quadratic.

AI explanation

For the first expression, expanding (x + 2) cubed yields x cubed + 6x squared + 12x + 8, and setting it equal to 2x cubed minus 2x gives a highest degree of 3, so it is not quadratic. For the second expression, expanding (x - 3)(2x + 1) yields 2x squared - 5x - 3, and setting it equal to x squared + 5x leaves x squared - 10x - 3 equals 0, making it quadratic. The third expression is already in the standard form x squared - 3x + 2 equals 0, making it quadratic. Because exactly two of the given equations are quadratic, the result is 2.

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