What is the nature of roots of quadratic equation if the value of its discriminant is equal to negative 16?
If the discriminant of the quadratic equation is negative, then the square root of the discriminant will be undefined.
What is the nature of the roots of the quadratic equation if the value of its discriminant is positive but not a perfect square?
irrational
If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational.
What is the nature of the roots of a quadratic equation when the discriminant?
The discriminant determines the nature of the roots of a quadratic equation. The word ‘nature’ refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary. Δ is the Greek symbol for the letter D. If Δ<0, then roots are imaginary (non-real) and beyond the scope of this book.
What does it mean when the discriminant is 0?
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. 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.
What is the nature of the roots of the quadratic equation *?
We can see, the discriminant of the given quadratic equation is positive but not a perfect square. Hence, the roots of a quadratic equation are real, unequal and irrational.
What is the nature of the roots of the quadratic equation if the value of the discriminant is less than zero?
imaginary
When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real. When discriminant is less than zero, the roots are imaginary.
What is the nature of the roots of the quadratic equation when b2 4ac is negative?
(ii) If b2 – 4ac is positive but not perfect square, the roots are irrational and unequal. If D = 0, i.e., b2 – 4ac = 0; the roots are real and equal. If D < 0, i.e., b2 – 4ac < 0; i.e., b2 – 4ac is negative; the roots are not real, i.e., the roots are imaginary.
What is the nature of the roots if B² 4ac 0?
The nature of roots in quadratic equation is dependent on discriminant(b2 – 4ac). (i) Roots are real and equal: If b2 -4ac = 0 or D = 0 then roots are real and equal. So the roots are equal which is 2.
What is the nature of the roots of the quadratic equation if the value of its?
When a, b, and c are real numbers, a ≠ 0 and the discriminant is a perfect square but any one of a or b is irrational then the roots of the quadratic equation ax2 + bx + c = 0 are irrational….Nature Of Roots.
| b2 – 4ac > 0 | Real and unequal |
|---|---|
| b2 – 4ac < 0 | Unequal and Imaginary |
| b2 – 4ac > 0 (is a perfect square) | Real, rational and unequal |
Which best describe the nature of roots of a quadratic equation if the value of its discriminant is 225?
Answer and Explanation: If the discriminant of a quadratic equation is 225, then the roots of that equation are rational.
What is the nature of roots if the discriminant is zero?
When discriminant is equal to zero, the roots are equal and real.
What is the nature of the roots of a quadratic equation?
How do you determine the nature of roots of quadratic equations?
To determine the nature of roots of quadratic equations (in the form ax^2 + bx +c=0), we need to calculate the discriminant, which is b^2 – 4 ac. When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real.
What does the discriminant of a quadratic equation reveal?
The discriminant of a quadratic equation reveals the nature of roots. The quadratic equation will have imaginary roots i.e α = (p + iq) and β = (p – iq). Where ‘iq’ is the imaginary part of a complex number
How many roots does the equation d = 0 have?
Since D>0, the equation will have two real and distinct roots. The roots are: Since D<0, the equation will have two distinct Complex roots. The roots are: Since D = 0, the equation will have two real and equal roots.
How do you find the roots of a graph with D=0?
D = 0: When D is equal to zero, the equation will have two real and equal roots. This means the graph of the equation will intersect x-axis at exactly one point. The roots can be easily determined from the equation 1 by putting D=0. The roots are: D < 0: When D is negative, the equation will have no real roots.