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When the discriminant is perfect square the answer to a quadratic equation will be?
Wiki User
∙ 12y ago
Rational.
Wiki User
∙ 12y ago
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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.
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.
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 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.
How can you determine if a general quadratic trinomial is factorable?
If the quadratic is written in the form ax2 + bx + c (where a not 0) then for it to be factorable, b2 - 4ac (the discriminant) must be a perfect square.
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.
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.
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 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 a perfect square are the solutions rational or irrational?
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.
What is discriminant in quadratic equation?
the square root of b squared minus 4 times a times c
Can the answer to a quadratic equation be a decimal?
Yes. You can calculate the two roots of a quadratic equation by using the quadratic formula, and because there are square roots on the quadratic formula, and if the radicand is not a perfect square, so the answer to that equation has decimal.
What is true about the solutions of a quadratic equation when the radicand of the quadratic formula is a perfect square?
The two solutions are coincident.
How can you determine if a general quadratic trinomial is factorable?
If the quadratic is written in the form ax2 + bx + c (where a not 0) then for it to be factorable, b2 - 4ac (the discriminant) must be a perfect square.
How do you figure out if a quadratic equation is a perfect square?
There are many ways: one is to factorise. If the quadratic is written as ax2 + bx + c then, if b2 = 4ac, the quadratic is a perfect square. It is (x - b/2a)2
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.
Explain why the roots of a quadratic equation are imaginary if the value of the discriminant is less than 0?
The square of any real number is non-negative. So no real number can have a negative square. Consequently, a negative number cannot have a real square root. If the discriminant is less than zero, the quadratic equation requires the square root of that negative value, which cannot be real and so must be imaginary.
