4-6 The Quadratic Formula and the Discriminant
Solve each equation by using the Quadratic Formula.
1. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
3. SOLUTION: Identify a, b, and c from the equation.
Substitute these values into the Quadratic Formula and simplify.
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5. Page 1
4-6 The
Quadratic Formula and the Discriminant
3. SOLUTION: Identify a, b, and c from the equation.
Substitute these values into the Quadratic Formula and simplify.
5. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
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7. Page 2
4-6 The Quadratic Formula and the Discriminant
5. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
7. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
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Page 3
4-6 The Quadratic Formula and the Discriminant
7. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
Complete parts a and b for each quadratic equation.
a. Find the value of the discriminant.
b. Describe the number and type of roots.
11. SOLUTION: a. Identify a, b, and c from the equation.
a = 2, b = –6 and c = 9.
Substitute the values in
and simplify.
b. The discriminant is negative, so there are two complex roots.
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13. Page 4
4-6 The Quadratic Formula and the Discriminant
Complete parts a and b for each quadratic equation.
a. Find the value of the discriminant.
b. Describe the number and type of roots.
11. SOLUTION: a. Identify a, b, and c from the equation.
a = 2, b = –6 and c = 9.
Substitute the values in
and simplify.
b. The discriminant is negative, so there are two complex roots.
13. SOLUTION: a. Identify a, b, and c from the equation.
a = 5, b = 2 and c = 4.
Substitute the values in
and simplify.
b. The discriminant is negative, so there are two complex roots.
Solve each equation by using the Quadratic Formula.
15. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
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Page 5
b. The
discriminant
is negative,
so Discriminant
there are two complex roots.
4-6 The
Quadratic
Formula
and the
Solve each equation by using the Quadratic Formula.
15. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
17. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
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Page 6
4-6 The
Quadratic Formula and the Discriminant
17. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
19. SOLUTION: 2
Write the equation in the form ax + bx + c = 0 and identify a, b, and c.
Substitute these values into the Quadratic Formula and simplify.
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Page 7
4-6 The Quadratic Formula and the Discriminant
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