Multiple choice

Find the nature of roots of the equation ${ x }^{ 2 }+ax+b=0$, where $a=2\sqrt{b}$ and $b> 3$

  1. Roots are equal

  2. Roots are unequal

  3. Imaginary

  4. None of these
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A Correct answer
Explanation

Discriminant D = a^2 - 4b. Given a = 2*sqrt(b), D = (2*sqrt(b))^2 - 4b = 4b - 4b = 0. When the discriminant is 0, the roots are real and equal.

AI explanation

For the equation x squared plus a x plus b equals 0, the discriminant determines the nature of the roots and is given by a squared minus 4 times b. Substituting a equals 2 times the square root of b into the discriminant yields 4 times b minus 4 times b, which equals 0. Because the discriminant is zero, the roots of the equation are equal.

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