Practice Relations Between Roots And Coefficients (2.7) - Algebra

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6 sample questions

Question 1.
What is the sum and product of the roots for the equation x² - 7x + 10 = 0?
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Use the formulas: Sum = -b/a and Product = c/a.
Question 2.
For the quadratic equation 5x² + 20x + 15 = 0, find the sum of the roots.
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Remember Sum of roots = -b/a; what is -20/5?
3Question 3.
What is the formula for the sum of roots in a quadratic equation?
- α + β = b/a
- α + β = -b/a
- α + β = c/a
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Think about how the coefficient 'b' is used in the formula.
4Question 4.
True or False: The product of the roots of the quadratic equation ax² + bx + c = 0 is given by c/a.
- True
- False
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Recall the product of roots relationship.
Question 5.
A quadratic equation has roots that are in the ratio of 2:1. If the sum of the roots is 12, write the equation.
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Set up a relationship using the given ratio and sum.
Question 6.
Determine the quadratic equation if the roots are -3 and 5.
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Use the reverse of the sum and product formulas to construct the equation.

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