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High School Mathematics
6.15 Forming a Quadratic Equation Using Its Roots

Let a and b be the roots of the quadratic equation, then the required equation is
x2 - (a + b)x + (a*b) = 0.

Example:
Find the quadratic equation whose roots are 5 and 3.
Solution:
Given that, roots of the equation are 5 and 3
Therefore, the required quadratic equation is
x2 - (a + b)x + (a*b) = 0.
Substituting the value of roots in the above equation we get the required equation.
x2 - (5+3)x + 5*3 = 0
x2 - 8x + 15 = 0.


Directions: Solve the following problems. Also write at least 5 examples of your own.
Q 1: Find the quadratic equation whose roots are 8 and -3.
x2 - 5x - 24
x2 + 5x - 24
x2 - 8x - 24
x2 - 11x - 24

Q 2: Find the quadratic equation whose roots are 3/2 and 5/2.
4x2 - 16x + 15
4x2 - 16x + 15
4x2 - 12x + 15
4x2 + 16x + 15

Q 3: Find the quadratic equation whose roots are 3/4 and 1/2.
8x2 + 10x + 3
8x2 - 10x - 3
8x2 - 10x + 3
8x2 - 8x + 3

Q 4: Find the quadratic equation whose roots are 7 and -2.
x2 + 5x - 14
x2 - 5x + 14
x2 - 9x - 14
x2 - 5x - 14

Q 5: Find the quadratic equation whose roots are 6 and 3.
x2 - 9x + 18
x2 - 9x + 9
x2 - 9x - 18
x2 + 9x + 18

Q 6: Find the quadratic equation whose roots are 9 and 1/2.
2x2 + 19x + 9
2x2 - 19x - 9
2x2 - 14x + 9
2x2 - 19x + 9

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Question 8: This question is available to subscribers only!


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