FRAMING A QUADRATIC EQUATION WITH GIVEN ROOTS
Framing a Quadratic Equation with Given Roots :
When two roots of a quadratic equation are given , the formula to form the quadratic equation is given by
x² - (sum of the roots)x + product of the roots = 0
If ∝ and ᵦ be the two roots of a quadratic equation are given , then the formula to form the quadratic equation is given by
x² - (α + β) x + αβ = 0
Example 1 :
Construct a quadratic equation whose two roots are -2 and -3
Solution :
Roots are α = -2 and β = -3
x² - (α + β) x + αβ = 0
|
α + β = -2 + (-3) = - 2 - 3 = -5 |
(α β) = -2(-3) = 6 |
x2 - (-5) x + (6) = 0
x2 + 5 x + 6 = 0
Example 2 :
Construct a quadratic equation whose two roots are 5 and -3.
Solution :
Roots are α = 5 and β = -3
|
α + β = 5 + (-3) = 5 - 3 = 2 |
α β = 5(-3) = -15 |
x² -2 x + (-15) = 0
x² - 2 x - 15 = 0
Example 3 :
Construct a quadratic equation whose two roots are 1 and 3
Solution :
Given roots are α = 1 and β = 3
|
α + β = 1 + 3 = 4 |
α β = 1(3) = 3 |
x² - 4 x + 3 = 0
Example 4 :
Construct a quadratic equation whose two roots are 24 and -3
Solution :
The given roots are α = 24 and β = -3
|
α + β = 24 + (-3) = 24 - 3 = 21 |
α β = 24(-3) = -72 |
x² - 21 x + (-72) = 0
x² - 21 x - 72 = 0
Example 5 :
Construct a quadratic equation whose two roots are -1 and -5
Solution :
The given roots are α = -1 and β = -5
|
α + β = -1 + (-5) = -1 - 5 = -6 |
α β = -1(-5) = 5 |
x² - (-6) x + 5 = 0
x² + 6 x + 5 = 0
Example 6 :
Construct a quadratic equation whose two roots are -7 and 5
Solution :
The given roots are α = -7 and β = 5
|
α + β = -7 + 5 = -2 |
α β = -7(5) = -35 |
x² - (-2) x + (-35) = 0
x² + 2 x - 35 = 0
After having gone through the stuff given above, we hope that the students would have understood how to frame a quadratic equation with given roots.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here
You can also visit the following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Division Word Problems Worksheet
Jul 09, 20 12:44 PM
Division Word Problems Worksheet
-
Addition Word Problems
Jul 07, 20 07:10 AM
Addition Word Problems
-
Division Word Problems
Jul 06, 20 11:17 PM
Division Word Problems with Step by Step Explanation
