Instructions: Calculate the discriminant, then state the number and type of solutions.10x2−x+7=010𝑥2−𝑥+7=0D=𝐷= Answer 1 Question 14
Question
Instructions: Calculate the discriminant, then state the number and type of solutions.10x2−x+7=010𝑥2−𝑥+7=0D=𝐷= Answer 1 Question 14
Solution
The discriminant of a quadratic equation is calculated using the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
In the given equation 10x² - x + 7 = 0, a = 10, b = -1, and c = 7.
Substituting these values into the formula, we get:
D = (-1)² - 4107 D = 1 - 280 D = -279
The discriminant is -279.
The discriminant tells us about the nature of the roots of the quadratic equation. If D > 0, the equation has two distinct real roots. If D = 0, the equation has two equal real roots (or one real root). If D < 0, the equation has two complex roots.
Since D = -279 is less than 0, the given equation has two complex roots.
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