Introduction :
In mathematics, a quadratic equation is one of a polynomial equation of the second degree. The general form is
ax^2+bx+c=0
Where x represent a variable, and a, b, and c, are the constants, with a ? 0. (If a = 0, the equation becomes a linear equation.). The constants a, b, and c, are called, the quadratic coefficient, the linear coefficient and the constant term or free term. The word "quadratic" comes from quadratus; it is the Latin word for "square." Quadratic equations can also be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula.
Source: wikipedia
Example problems on Quadratic equations with square roots:
Example 1:
Determine all real solutions to the equation
Sqrt (x + 1) = 4
Solution:
Given equation is
sqrt (x + 1) = 4
Squaring on both sides, then the above equation becomes
[sqrt (x + 1)]^2 = 4^2
Simplify the above equation
x + 1 = 16
Solve for x.
x = 15
NOTE: Because we squared both sides not including putting any conditions, extraneous solutions may be introduced, checking the solutions is necessary.
Check the left side (LS) of the given equation when x = 15
LS = sqrt (x + 1) = sqrt (15 + 1) = 4
Check the right Side (RS) of the given equation when x = 15
RS = 4
When x = 15, the left and the right sides of the given equation are equal: x = 15 is a solution to the given equation.
Example 2:
Determine all real solutions of the equation
Sqrt (3 x + 1) = x - 3
Solution:
Given equation is
sqrt ( 3 x + 1) = x - 3
Squaring on both sides, then the above equation becomes
[sqrt ( 3 x + 1) ]^2 = (x - 3)^2
Simplify the above equation
3 x + 1 = x^2 - 6 x + 9
Rewrite the above equation in factor form.
x^2 - 9 x + 8 = 0
The above form is a quadratic equation with 2 solutions
x = 8 and x = 1
Practice problems on quadratic equations with square roots:
1) Determine the real value of the given quadratic equation with square roots.
Sqrt (2 x + 15) = 5
Answer: x = 5
2) Determine the real value of the given quadratic equation with square roots.
Sqrt (4 x - 3) = x – 2
Answer: x = 7
In mathematics, a quadratic equation is one of a polynomial equation of the second degree. The general form is
ax^2+bx+c=0
Where x represent a variable, and a, b, and c, are the constants, with a ? 0. (If a = 0, the equation becomes a linear equation.). The constants a, b, and c, are called, the quadratic coefficient, the linear coefficient and the constant term or free term. The word "quadratic" comes from quadratus; it is the Latin word for "square." Quadratic equations can also be solved by factoring, completing the square, graphing, Newton's method, and using the quadratic formula.
Source: wikipedia
Example problems on Quadratic equations with square roots:
Example 1:
Determine all real solutions to the equation
Sqrt (x + 1) = 4
Solution:
Given equation is
sqrt (x + 1) = 4
Squaring on both sides, then the above equation becomes
[sqrt (x + 1)]^2 = 4^2
Simplify the above equation
x + 1 = 16
Solve for x.
x = 15
NOTE: Because we squared both sides not including putting any conditions, extraneous solutions may be introduced, checking the solutions is necessary.
Check the left side (LS) of the given equation when x = 15
LS = sqrt (x + 1) = sqrt (15 + 1) = 4
Check the right Side (RS) of the given equation when x = 15
RS = 4
When x = 15, the left and the right sides of the given equation are equal: x = 15 is a solution to the given equation.
Example 2:
Determine all real solutions of the equation
Sqrt (3 x + 1) = x - 3
Solution:
Given equation is
sqrt ( 3 x + 1) = x - 3
Squaring on both sides, then the above equation becomes
[sqrt ( 3 x + 1) ]^2 = (x - 3)^2
Simplify the above equation
3 x + 1 = x^2 - 6 x + 9
Rewrite the above equation in factor form.
x^2 - 9 x + 8 = 0
The above form is a quadratic equation with 2 solutions
x = 8 and x = 1
Practice problems on quadratic equations with square roots:
1) Determine the real value of the given quadratic equation with square roots.
Sqrt (2 x + 15) = 5
Answer: x = 5
2) Determine the real value of the given quadratic equation with square roots.
Sqrt (4 x - 3) = x – 2
Answer: x = 7
No comments:
Post a Comment