Multiple choice

If a and b are the roots of the equation $\displaystyle x^{2}-1=0$ the form of quadratic equation whose roots are 2a and 2b will be-

  1. $\displaystyle x^{2}-4\sqrt{2}=0$
  2. $\displaystyle x^{2}+4=0$
  3. $\displaystyle x^{2}-4=0$
  4. $\displaystyle x^{2}+4\sqrt{2}=0$
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C Correct answer
Explanation

The roots of the equation x^2 - 1 = 0 are 1 and -1. Doubling these roots gives the new roots as 2 and -2. The quadratic equation with these new roots is (x - 2)(x + 2) = x^2 - 4 = 0.

AI explanation

For the equation x^2 - 1 = 0, the roots are a = 1 and b = -1. The new roots are 2a = 2 and 2b = -2. A quadratic equation with roots r1 and r2 is given by x^2 - (r1 + r2)x + r1*r2 = 0. The sum of the new roots is 2 + (-2) = 0 and their product is 2*(-2) = -4, making the equation x^2 - 4 = 0.

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