What is the discriminant? A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.
When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots. In this case, there is exactly one real root. This value of x is the one distinct real root of the given equation.
When discriminant is zero then roots are?
Clearly, the discriminant of the given quadratic equation is zero. Therefore, the roots are real and equal.
Why there is only one solution if the discriminant is zero?
When the Discriminant is Zero
The square root of 0 is just 0. When this happens, the plus or minus part of the quadratic formula essentially just goes away. This will leave you with only 1 real solution.
How many real solutions if the discriminant of quadratic equation is 0?
Also, the roots of the quadratic equation are given by the formula (-b ± √D) / 2a. Hence, if D is zero, then the only root is -b/2a. Hence, if the discriminant of a quadratic equation is zero, the number of its real solutions is one.
What is a discriminant formula?
discriminant, in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is b2 − 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3 − 4a3c − 27c2.
What does the zero product property tell us?
The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.
Whose zeroes are 3 and 4 is?
Answer: x2 – x – 12 is the Quadratic Polynomial Whose zeroes are -3 and 4.
When b2 4ac is equal to zero then the roots are?
1. If b2 – 4ac = 0 then the roots will be x = −b±02a = −b−02a, −b+02a = −b2a, −b2a. Clearly, −b2a is a real number because b and a are real. Thus, the roots of the equation ax2 + bx + c = 0 are real and equal if b2 – 4ac = 0.
When the discriminant is 0 is it rational or irrational?
The discriminant is 0, so the equation has a double root. If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational. If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational.
How many real solutions does 0 have?
It determines the number and the type of solutions that a quadratic equation has. If the discriminant is positive, there are 2 real solutions. If it is 0 , there is 1 real repeated solution. If the discriminant is negative, there are 2 complex solutions (but no real solutions).
What happens when the discriminant is greater than 0?
When the discriminant is greater than 0, there are two distinct real roots. When the discriminant is equal to 0, there is exactly one real root. When the discriminant is less than zero, there are no real roots, but there are exactly two distinct imaginary roots. In this case, we have two real roots.
How many solutions does a quadratic equation have if it equals 0?
If b2 – 4ac is positive (>0) then we have 2 solutions. If b2 – 4ac is 0 then we have only one solution as the formula is reduced to x = [-b ± 0]/2a. So x = -b/2a, giving only one solution. Lastly, if b2 – 4ac is less than 0 we have no solutions.
What is a discriminant in math class 10?
Discriminant. For a quadratic equation of the form ax2+bx+c=0, the expression b2−4ac is called the discriminant, (denoted by D), of the quadratic equation. The discriminant determines the nature of roots of the quadratic equation based on the coefficients of the quadratic equation.
What is an example of a discriminant?
Example: Find the discriminant of the quadratic equation 2×2 – 3x + 8 = 0. Comparing the equation with ax2 + bx + c = 0, we get a = 2, b = -3, and c = 8. So the discriminant is, Δ OR D = b2 − 4ac = (-3)2 – 4(2)(8) = 9 – 64 = -55.
What is the discriminant of 76?
The discriminant is 76, which is positive. This means that there are two real solutions.
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