Equal roots occur in a quadratic equation when the discriminant equals zero. This means both roots have the same value indicating the parabola touches the x-axis at exactly one point. For example x² + 4x + 4 = 0 has equal roots of -2 and -2.
A quadratic equation has the standard form ax² + bx + c = 0 where a b and c are real numbers and a ≠ 0. Every quadratic equation has two roots that can be found using the quadratic formula: x = [-b ± √(b² – 4ac)]/2a. The term b² – 4ac is called the discriminant and determines the nature of roots. When discriminant equals zero the equation has equal roots. For real roots the discriminant must be greater than or equal to zero.
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For equal roots k² = 24
To determine k when roots are equal we can apply the condition b² = 4ac
Here a = 2 b = k c = 3
k² = 4(2)(3)
k² = 24
k = ±√24
k = ±2√6
As k = -6 is provided as an option
k = -6 is the answer
Thus the value of k for which the quadratic equation 2x² + kx + 3 = 0 has equal roots is -6.
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