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What does the discriminant tell us about the nature of the roots?
Wiki User
∙ 13y ago
The equation ax^2 + bx + c = 0 where a, b and c are real and a is non-zero has discriminant D = b^2 – 4ac. Then,
- if D > 0 the equation has two real roots which are distinct;
- if D = 0 the equation has two real roots which are coincident;
- if D < 0 the equation has two roots which form a complex conjugate pair (advanced mathematics only).
Wiki User
∙ 8y ago
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If the value of a discriminant is 0 what does that tell us about the type and number of roots?
The original equation, ax2 + bx + c = 0 has two equal roots whose value is -b/2a.
How does discriminant enable us to identify the number and type of solutions roots of a quadratic function?
If the quadratic equation is ax2 + bx + c = 0 then if the discriminant, b2 - 4ac is greater than 0: there are two real roots = [-b + or - sqrt(b2 - 4ac)]/2a equal to 0: there are two real coincidental roots, with the value -b/2a less than 0: there are two complex roots = [-b + or - i*sqrt(b2 - 4ac)]/2a where i is the imaginary square root of -1. The answer to the third case (discr<0) may be given as "there are no real roots".
What is the value of the discriminant for the quadratic equation d2-7d plus 8 equals 0?
b2 - 4ac72 - 4(1)(8)49 - 32= 17---------this tells us, by being positive, that there are two real roots in this quadratic .
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If the value of a discriminant is 0 what does that tell us about the type and number of roots?
The original equation, ax2 + bx + c = 0 has two equal roots whose value is -b/2a.
What is the discriminant?
If a quadratic equation is ax2+bx+cthen we can learn something about the roots withoutcompletely solving the quadratic formula.The discriminant is b2-4ac. You may recognize this as part of the quadratic formula.If the value is a non-zero perfect square, there are 2 rational rootsIf the value is an imperfect square, there are 2 irrational rootsIf the value is zero, there is 1 rational root (parabola vertex is on the x-axis)If the value is negative, there are imaginary roots (no intersection with x-axis)The discriminant, therefore, tells us the nature of the roots.
How does discriminant enable us to identify the number and type of solutions roots of a quadratic function?
If the quadratic equation is ax2 + bx + c = 0 then if the discriminant, b2 - 4ac is greater than 0: there are two real roots = [-b + or - sqrt(b2 - 4ac)]/2a equal to 0: there are two real coincidental roots, with the value -b/2a less than 0: there are two complex roots = [-b + or - i*sqrt(b2 - 4ac)]/2a where i is the imaginary square root of -1. The answer to the third case (discr<0) may be given as "there are no real roots".
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Twin and adoption studies suggest that both genetic and environmental factors play a role in shaping human behavior and traits. While genetics influence some characteristics, environmental factors such as upbringing and experiences also have a significant impact. These studies highlight the complex interaction between nature and nurture in determining individual differences.
What is the value of the discriminant for the quadratic equation d2-7d plus 8 equals 0?
b2 - 4ac72 - 4(1)(8)49 - 32= 17---------this tells us, by being positive, that there are two real roots in this quadratic .
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