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faust18 [17]
2 years ago
13

Determine the number and types of solutions for 6m^2-3m-4=0

Mathematics
1 answer:
Anna11 [10]2 years ago
4 0

Answer:

2 real solutions

Step-by-step explanation:

Remember this messy thing?

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

The <em>quadratic formula</em>, as it's called, gives us the roots to any quadratic equation in standard form (ax² + bx + c = 0). The information on the <em>type</em> of roots is contained entirely in that bit under the square root symbol (b² - 4ac), called the <em>discriminant</em>. If it's non-negative, we'll have <em>real</em> roots, if it's negative, we'll have <em>complex roots</em>.

For our equation, we have a discrimant of (-3)² - 4(6)(-4) = 9 + 96 = 105, which is non-negative, so we'll have real solutions, and since quadratics are degree 2, we'll have exactly 2 real solutions.

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