How do you find equal roots?
A quadratic equation has equal roots iff its discriminant is zero.A quadratic equation has equal roots iff these roots are both equal to the root of the derivative..
What are two equal real roots?
Equal or double roots. If the discriminant b2 – 4ac equals zero, the radical in the quadratic formula becomes zero. In this case the roots are equal; such roots are sometimes called double roots. Therefore, the roots are equal.
What is the formula for sum of roots?
Example: What is an equation whose roots are 5 + √2 and 5 − √2. When a=1 we can work out that: Sum of the roots = −b/a = -b. Product of the roots = c/a = c.
How do you prove that an equation has real roots?
To find a value of k that makes the roots rational and unequal the discriminant must be greater than 0 and a perfect square. So if k=0 or k=5 the roots will be rational and unequal. Prove that the roots of the equation x2−(a+b)x+ab−p2=0 are real for all real values of a, b and p.
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.