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When the discriminant is a perfect square are the solutions rational or irrational?
Wiki User
∙ 11y ago
The "discriminant" here refers to the part of the quadratic equation under the radical (square root) sign. When it is a perfect square, the square root is also a perfect square, so the radical goes away, leaving only rational numbers. So, when the discriminant is a perfect square, the solutions are (usually) rational. Unless, of course, some other part of the result is irrational. For example, if the coefficient of the x2 term ("a" in the quadratic formula) is pi, and the constant term is 1/pi, the discriminant will turn out to be 4 (4ac = 4 * pi * 1/pi = 4), which is a perfect square, but solutions will be irrational anyway because the denominator becomes 2pi, and pi is irrational.
Wiki User
∙ 11y ago
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Are non perfect squares irrational?
No. 2.25 is not a perfect square but it is rational.
Is a non perfect square irrational?
No. 2.25 = 1.5^2 is a non-perfect square but it is rational.
Is 6 square root of 26 rational number?
It is irrational. * The square root of any positive integer, except of a perfect square, is irrational. * The product of an irrational number and a rational number (except zero) is irrational.
Is the square root of 97 rational or irrational?
The square root of ANY positive integer is either a whole number, or an irrational number. Only the perfect squares have whole number square roots; all the rest are irrational. 97 is not a perfect square therefore √97 is irrational.
Are radical expressions irrational?
If the value applied in the radical is not a perfect square, it is irrational. 25; 400; and 625 are perfect squares and are rational when applied in a radical.
What is true of the discriminant when the two real number solutions to a quadratic equation are rational numbers?
The discriminant must be a perfect square or a square of a rational number.
How do you know if a quadratic equation can be factored?
The answer depends on what the factors will be. For example, every quadratic can be factored if you allow complex numbers. If not, then it helps to use the discriminant. If it is positive, there are two real factors or solutions. If that positive number is a perfect square, then the factors are rational numbers. If not, they are real but not rational (irrational). If the discriminant is 0, there is one real solution. Lastly, if it is negative, there are no real solutions.
What is true of the disciminant when the two real numbers solutions to a quadratic equation are irrational numbers?
In that case, the discriminant is not a perfect square.
What does the discriminant have to be in order for the roots of a quadratic to be irrational?
The discriminant must be a positive number which is not a perfect square.
When the discriminant is perfect square the answer to a quadratic equation will be?
Rational.
Is negative 90 squared... this is the one with the box around it... rational or irrational and are perfect squares rational or irrational?
-90 squared is rational - it is +8100. All perfect squares are not only rational but they are integers.
Is the perfect square of 64 a rational or irrational number?
It is a rational number - as are ALL perfect squares.
Are non perfect squares irrational?
No. 2.25 is not a perfect square but it is rational.
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.
Is the square root of 4 irrational or rational?
It is rational. The root of a perfect square, such as 4, is rational; the root of any positive integer that is not a perfect square is an irrational number.
Is the square root of -144 rational or irrational?
It is irrational, because it is not a perfect square. For example, if you have a number that is perfect like the square root of 100, it would be 10, which is a rational number. An irrational number like 16.4 which would be a not so accurate result like 6.447583839, those are irrational numbers. Hope this helps!
What is an irrational number that is a perfect square?
That isn't possible. Rational numbers either terminate or have a repeating pattern, and irrational numbers are all the rest. Perfect squares terminate, therefore they are rational.
