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Yes. If the discriminant (of a quadratic equation) is...
- Positive: There are two real roots.
- Zero: There is a single "double" root. ("Double" means that if you factor, you will have a repeated factor.)
- Negative: There are two complex roots (and no real roots).
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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 is negative the equation has?
No real roots but the roots are a pair of complex conjugates.
What is the discriminant of x2 3x 4?
The discriminant of x2+3x+4 is -7 therfore it has no real roots.
How do you find the discriminant and number of real solutions to a quadratic equation?
To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, you use the formula Δ = b^2 - 4ac. The discriminant helps determine the nature of the roots: if Δ > 0, there are two distinct real roots; if Δ = 0, there is one real root (a repeated root); and if Δ < 0, there are no real roots (two complex conjugate roots). The number of real solutions is directly related to the discriminant's value.
What use the discriminant to determine the nature of the roots of x2 plus 2x plus 5 equals 0?
No real 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 solutions will a problem have if the discriminant is positive?
Two real roots.
How to tell if there are no real roots?
The real roots of what, exactly? If you mean a square trinomial, then: If the discriminant is positive, the polynomial has two real roots. If the discriminant is zero, the polynomial has one (double) real root. If the discriminant is negative, the polynomial has two complex roots (and of course no real roots). The discriminant is the term under the square root in the quadratic equation, in other words, b2 - 4ac.
What is true about a quadratic equation when the discriminant of the equation is positive?
It will then have 2 different roots If the discriminant is zero than it will have have 2 equal roots
What is the discriminant and how does it help in knowing how many solutions a quadratic equations will have?
Put the equation into ax²+bx+c=0 form. The discriminant is b²-4ac. If it is negative, there are no real roots. If it is 0, there is one real root. If it is positive, there are 2 real roots. ■
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.
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.
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 greater than 0 how many real roots are there?
There will be 2 real roots
What is the nature of the roots of 4x2 plus 15x plus 10 equals 0?
The discriminant of the equation ... (b2-4ac) = (225-160) ... is real and positive, so the roots are real and unequal.
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.
What is the discriminant in a math equation?
In a quadratic equation of the form ax2+bx + c = 0, the discriminant is b2-4ac. It determines the nature of the roots of the equation. If it is positive, there are two real roots; if is negative, there are two complex roots; if it is zero, there is one real root, often called a double root. Both real roots are rational if and only the discriminant is a perfect square.
