Direction: Using the values of a, b, and c of each of the following quadratic equation solve for the sum and product of roots. Check your answer by using the roots of the quadratic equation. Then answer the question below.
Quadratic Equation Sum of the Roots Product of the Roots Roots
1.) X2 + 3x - 10=0 2.) X2 – 4x - 21=0 3.) X2 – 6x - 7=0 4.) -2x2 - 8x + 10=0 5.) 6x2 - 7x + 2=0
Answers
The sum and product of roots are
1. - 3, -10
2. 4, -21
3. 6, - 7
4. 4, 5
5. 7/2, 1/3
Given:
1. x² + 3x - 10 = 0
2. x² – 4x - 21 = 0
3. x² – 6x - 7 = 0
4. -2x² - 8x + 10 = 0
5. 6x²- 7x + 2 = 0
To find:
Using the values of a, b, and c of each of the following quadratic equations solve for the sum and product of roots.
Solution:
Formula used:
Sum and product of roots for Quadratic Equation ax²+bx+c = 0
Sum of roots = (coefficient of x)/ (coefficient of x²) = −b/a
Product of roots = (constant term)/ (coefficient of x2) = c/a
1. x² + 3x - 10 = 0
Compare the given equation with ax²+bx+c = 0
=> a = 1, b = 3 and c = - 10
Sum of roots = -3/1 = - 3
Product of roots = -10/1 = -10
2. x² – 4x - 21 = 0
Compare the given equation with ax²+bx+c = 0
=> a = 1, b = -4 and c = - 21
Sum of roots = -(-4)/1 = 4
Product of roots = (-21)/1 = -21
3. x² – 6x - 7 = 0
Compare the given equation with ax²+bx+c = 0
=> a = 1, b = - 6 and c = - 7
Sum of roots = -(-6)/1 = 6
Product of roots = (-7)/1 = - 7
4. -2x² - 8x + 10 = 0
Compare the given equation with ax²+bx+c = 0
=> a = -2, b = - 8 and c = 10
Sum of roots = -(-8)/2 = 4
Product of roots = (10)/2 = 5
5. 6x²- 7x + 2 = 0
Compare the given equation with ax²+bx+c = 0
=> a = -6, b = - 7 and c = 2
Sum of roots = -(-7)/2 = 7/2
Product of roots = (2)/6 = 1/3
Therefore,
The sum and product of roots are
1. - 3, -10
2. 4, -21
3. 6, - 7
4. 4, 5
5. 7/2, 1/3
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