Multiple choice

Find the nature of roots of the following equations: (i) x2 + 9x + 27 = 0 (ii) 6x2 - 13x - 5 = 0

  1. (i) Real (ii) Real

  2. (i) Real (ii) Imaginary

  3. (i) Imaginary (ii) Real

  4. (i) Imaginary (ii) Imaginary
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Nature of roots is determined by the discriminant D = b^2 - 4ac. (i) D = 9^2 - 4(1)(27) = 81 - 108 = -27 (Imaginary). (ii) D = (-13)^2 - 4(6)(-5) = 169 + 120 = 289 (Real).

AI explanation

To find the nature of the roots, we use the discriminant formula, which is b^2 - 4ac. For the first equation x^2 + 9x + 27 = 0, the discriminant is 9^2 - 4(1)(27), which equals 81 - 108 = -27, making the roots imaginary since the value is negative. For the second equation 6x^2 - 13x - 5 = 0, the discriminant is (-13)^2 - 4(6)(-5), which equals 169 + 120 = 289, making the roots real since the value is positive. Therefore, the first equation has imaginary roots and the second has real roots.

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