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What does the discriminant have to be in order for the roots of a quadratic to be irrational?
Wiki User
∙ 10y ago
The discriminant must be a positive number which is not a perfect square.
Wiki User
∙ 8y ago
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What are quadratic equations with real roots?
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
Which of the folllowing indicates that the roots of a quadratic are irrational?
The discriminant is the expression inside the square root of the quadratic formula. For a quadratic ax² + bx + c = 0, the quadratic formula is x = (-b +- Sqrt(b² - 4ac))/(2a). The expression (b² - 4ac) is the discriminant. This can tell a lot about the type of roots. First, if the discriminant is a negative number, then it will have two complex roots. Because you have a real number plus sqrt(negative) and real number minus sqrt(negative). You asked about irrational. If the discrimiant is a perfect square number {like 1, 4, 9, 16, etc.} then the quadratic will have two distinct rational roots (which are real numbers). If the discriminant is zero, then you will have a double root, which is a real rational number. So if the discrimiant is positive, but not a perfect square, then the roots will be irrational real numbers. If the discriminant is a negative number which is not the negative of a perfect square, then imaginary portion of the complex number will be irrational.
How does the discriminant affect the roots of a quadratic equation?
If the discriminant is negative, the roots will be two unreal complex conjugates. If the discriminate is positive the roots will be real.
How many real roots exist if the discriminant of the eqation0?
If the discriminant of a quadratic equation is 0 then it has two equal real roots.
Why the discriminant of a quadratic is useful in algebra?
Because the square root of the discriminant is a component of the roots of the equation.
What are quadratic equations with real roots?
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
Which of the folllowing indicates that the roots of a quadratic are irrational?
The discriminant is the expression inside the square root of the quadratic formula. For a quadratic ax² + bx + c = 0, the quadratic formula is x = (-b +- Sqrt(b² - 4ac))/(2a). The expression (b² - 4ac) is the discriminant. This can tell a lot about the type of roots. First, if the discriminant is a negative number, then it will have two complex roots. Because you have a real number plus sqrt(negative) and real number minus sqrt(negative). You asked about irrational. If the discrimiant is a perfect square number {like 1, 4, 9, 16, etc.} then the quadratic will have two distinct rational roots (which are real numbers). If the discriminant is zero, then you will have a double root, which is a real rational number. So if the discrimiant is positive, but not a perfect square, then the roots will be irrational real numbers. If the discriminant is a negative number which is not the negative of a perfect square, then imaginary portion of the complex number will be irrational.
When can you say that he discriminant don't have roots?
If the discriminant b2-4ac of a quadratic equation is less than zero then it will have no roots
What is a discriminant in a quadratic equation?
General form of a quadratic equation is: ax2+b+c = 0 The discriminant is: b2-4ac If the discriminant equals zero then there are two equal roots If the discriminant is greater than zero then there are two different roots If the discriminant is less than zero then there are no real roots
What are 3 outcomes for the discriminant?
If the discriminant of a quadratic equation is zero then it has equal roots. If the discriminant is greater than zero then there are two different roots. If the discriminant is less than zero then there are no real roots.
If the discriminant of an equation is 0?
If the discriminant of a quadratic equation is zero then it has two identical roots.
How does the discriminant affect the roots of a quadratic equation?
If the discriminant is negative, the roots will be two unreal complex conjugates. If the discriminate is positive the roots will be real.
How many real roots exist if the discriminant of the eqation0?
If the discriminant of a quadratic equation is 0 then it has two equal real roots.
Why the discriminant of a quadratic is useful in algebra?
Because the square root of the discriminant is a component of the roots of the equation.
What can the discriminant tell you about a quadratic equation?
It can tell you three things about the quadratic equation:- 1. That the equation has 2 equal roots when the discriminant is equal to zero. 2. That the equation has 2 distinctive roots when the discriminant is greater than zero. £. That the equation has no real roots when the discriminant is less than zero.
How many real roots exist if the discriminant of the equation plus 0?
If the discriminant of a quadratic equal is zero then it will have two equal roots.
When can you say that the discriminant don't have root?
If the discriminant of a quadratic equation is less than zero then it will have no real roots
