Quadratic Function Roots

Introduction to quadratic function:

A quadratic function, in mathematics, is a polynomial function of the form



The graph of a quadratic function is a parabola whose major axis is parallel to the y-axis.

The quadratic function has the highest degree of 2.

If the quadratic function ax2 + bx + c = 0, then it becomes quadratic equation.

Roots of Quadratic Functions:

If  the coefficients of quadratic function a, b and c are real and complex, then the roots of quadratic function will be

x = `(-b+-sqrt(b^2 - 4ac))/(2a)`

The above formula is called quadratic formula.

The root of quadratic functions are different real numbers, if b2 - 4ac > 0. i.e., The function has two real roots.
The root of quadratic functions are equal real numbers, if b2 - 4ac = 0. i.e., The function has one real root.
The root of quadratic functions are imaginary numbers, if b2 - 4ac < 0. i.e., The function has no real roots.
The expression b2 - 4ac is called the discriminant of a quadratic function.Understanding what is rotational symmetry is always challenging for me but thanks to all math help websites to help me out.

Example Problems to Learn Roots of Quadratic Function:

Example 1:

Find the root of quadratic function f(x) = x2 + 7x - 30.

Solution:

Step 1: Given quadratic function

f(x) = x2 + 7x - 30

Step 2: Rewrite the term ' 7x ', as ' 10x - 3x ', we get

f(x) = x2 + 10x - 3x - 30

Step 3: Take the common terms outside

f(x) = x(x + 10) - 3(x + 10)

f(x) = (x - 3)(x + 10)

Step4: Equate each function to zero to find roots

x - 3 = 0                                                             x + 10 = 0

Add 3 on both side, we get                                       Subtract 10 on both side, we get

x = 3                                                                     x = - 10

Step 5: Solution

The roots of given quadratic functions are 3 and - 10

Example 2:

Find the root of quadratic function f(x) = x2 + 16x + 63.

Solution:

Step 1: Given quadratic function

f(x) = x2 + 16x + 63

Step 2: Rewrite the term ' 16x ', as ' 9x + 7x ', we get

f(x) = x2 + 9x + 7x + 63

Step 3: Take the common terms outside

f(x) = x(x + 9) + 7(x +9)

f(x) = (x + 9)(x + 7)

Step4: Equate each function to zero to find roots

x + 9 = 0                                                             x + 7 = 0

Subtract 9 on both side, we get                                       Subtract 7 on both side, we get

x = - 9                                                                     x = - 7

Step 5: Solution

The roots of given quadratic functions are - 9 and - 7.