Multiple choice

Determine the nature of the roots of the given equation from their discriminants. $2y^{2}\, +\, 11y\, -\, 7\, =\, 0$

  1. Real and equal

  2. Real and unequal

  3. One real and one imaginary

  4. Both imaginary
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 2y^2 + 11y - 7 = 0, the discriminant D = b^2 - 4ac = 11^2 - 4(2)(-7) = 121 + 56 = 177. Since D > 0 and not a perfect square, the roots are real and unequal.

AI explanation

Apply the discriminant formula D equals b squared minus 4ac. For the equation 2y squared plus 11y minus 7 equals 0, D equals 11 squared minus 4 times 2 times -7, which simplifies to 121 plus 56, or 177. Since the discriminant 177 is greater than zero, the roots are real and unequal.

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