Press "Enter" to skip to content

What is the maximum number of solutions a square root equation can have?

The Discriminant As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

Do square roots always have 2 answers?

Simply because every number has two square roots. If we define “square root” to mean “a number which, when multiplied by itself, gives the target product as a result,” then we are inevitably faced with the fact that there are two numbers which do so, one negative and one positive.

Is there only one solution to a square root?

Zero is the only number that has only one unique real square root.

How did you solve the roots of an equation?

The roots of any quadratic equation is given by: x = [-b +/- sqrt(-b^2 – 4ac)]/2a. Write down the quadratic in the form of ax^2 + bx + c = 0. If the equation is in the form y = ax^2 + bx +c, simply replace the y with 0. This is done because the roots of the equation are the values where the y axis is equal to 0.

How do you find the roots on a calculator?

The TI graphing calculator can be used to find the real roots of an equation….TI-85 / TI-86

  1. Press Graph.
  2. Press More and then Math (F1)
  3. Press Lower (F1).
  4. Press Upper (F2).
  5. Press Root (F3).

How did you determine the roots of each quadratic equation?

To determine the nature of roots of quadratic equations (in the form ax^2 + bx +c=0) , we need to caclulate the discriminant, which is b^2 – 4 a c. When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real.

How do you find the nature of the roots Class 10?

The discriminant is said to be the part of the quadratic formula under the square root. x = [-b ± √(b²-4ac)] / 2a. The discriminant can be zero, positive or negative and it states the number of solutions can be given to the quadratic equation.

What are the roots of the equation in number 1 What do the roots represent?

Answer: The roots are ± 12. Roots represents the square root and finding a solution to an equation.

What does it mean when an equation has a root?

Root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.

How do you find the real and imaginary roots?

Imaginary roots appear in a quadratic equation when the discriminant of the quadratic equation — the part under the square root sign (b2 – 4ac) — is negative. If this value is negative, you can’t actually take the square root, and the answers are not real.

How do you know if roots are imaginary?

If the roots of a quadratic equation are imaginary, they always occur in conjugate pairs. Imaginary or complex roots will occur when the value under the radical portion of the quadratic formula is negative. Notice that the value under the radical portion is represented by “b2 – 4ac”.

What are real and complex roots?

The Fundamental Theorem of Algebra says that a polynomial of degree n has exactly n roots. If those roots are not real, they are complex. But complex roots always come in pairs, one of which is the complex conjugate of the other one.

What do complex roots mean?

These are the two places in which the sketched graph crosses the x-axis. This leads us to roots of a quadratic equation that does not cross the x-axis. These roots are known as complex (imaginary) roots. An example of a quadratic drawn on a Page 5 coordinate plane with complex roots is shown in Figure 3.

Is zero a complex root?

The Fundamental Theorem of Algebra states that every polynomial of degree one or greater has at least one root in the complex number system (keep in mind that a complex number can be real if the imaginary part of the complex root is zero).

Can a polynomial have 3 imaginary roots?

Since the equation has at most three distinct roots, it follows that it cannot have three distinct complex nonreal roots. Your argument is an almost correct proof of the fact that a cubic equation cannot have three complex (non-real) roots.

How do you know if a polynomial has complex roots?

If the polynomial has Real coefficients, then any Complex zeros will occur in Complex conjugate pairs. So the number of non-Real zeros will be even. If the coefficients are Real then we can find out some more things about the zeros by looking at the signs of the coefficients.

How many distinct and real roots can a degree n polynomial have?

How many distinct and real roots can an $$ n th-degree polynomial have? Teacher Tips: Sample Answer: An $$ n th degree polynomial can have up to $$ n distinct and real roots. (If $$ n is odd, the function must have at least one distinct and real root.)