Question

1. If the roots of a quadratic equation are m and n, what is the product of the roots (mn)

in terms of the coefficients a, b, and c?
a. mn = -c/a
b. mn = -c/a
c. mn = b/a
d. mn = -b/a
Answer:
2. If the quadratic equation px2 — 6x + 9 = 0 has roots a and b, what is the value of a + b?
a. a + b = 6/p
b. a + b = -6/p
c. a + b = 9/p
d. a + b = -6/p
Answer:

3. If the roots of a quadratic equation are p and q, what is the value of p2 + q2 in terms
of the coefficients a, b, and c?
a. p2 + q2 = b2 / a2
b. p2 + q2 = (b2— 2ac) / a2
c. p2 + q2 = (b2 + 2ac) / a2
d. p2 + q2 = (b2 — 4ac) / a2
Answer:

4. If the quadratic equation 2x2 — 5x + k = 0 has roots α and β, what is the sum of the
roots (α+β)?
a. α+β = -5/2
b. α+β = 5/2
c. α+β = k/2
d. α+β = 2/5
Answer:

5. If a quadratic equation has roots x = 2 and x = -3, what is the equation in the form αx2
+ bx + c= 0
a. 2x2 + x — 6 = 0
b. 2x2 — x — 6 = 0
c. 2x2 — 5x — 6 = 0
d. 2x2 — 5x — 6 = 0
Answer:
6. For a quadratic equation αx2 + bx + c = 0, if b2 — 4ac > 0, what does this indicate
about the roots of equation?
a. The roots are real and unequal.
b. The roots are real and equal.
c. The roots are complex and conjugates.
d. The roots have no real roots.
Answer:
7. If the discriminant (Δ) of a quadratic equation is zero, what can you conclude about
the roots of the equation?
a. The roots are real and unequal.
b. The roots are real and equal.
c. The roots are complex and conjugates.
d. The roots are imaginary.
Answer:
8. What is the relationship between the sum of the roots (α+β) and the coefficients of a
quadratic equation α2 + bx + c = 0
a. α+β = -b/a
b. α+β = c/a
c. α+β = -c/a
d. α+β = b/a
Answer:
9. What is the relationship between the coefficients a, b, and c when the quadratic
equation αx2 + bx + c= 0 has no real roots?
a. b2 — 4ac = 0
b. b2 — 4ac > 0
c. b2 — 4ac < 0
d. a2 — 4bc = 0
Answer:
10. If a quadratic equation has roots α and β, what is the product of the roots (α •β) in
terms of the coefficients a, b, c?
a. α •β= b/a
b. α •β= -c/a
c. α •β = c/a
d. α •β = -b/a
Answer:


(Due November 28 ) Thank uuu!

Answer 1

The product of roots of a quadratic equation is given by -c/a, and the sum of roots is given by -b/a. For real and unequal roots, b² - 4ac should be greater than zero. When the discriminant is zero, the quadratic equation has real and equal roots.

Step-by-step explanation:

The product of the roots (mn) of a quadratic equation ax² + bx + c = 0 is mn = -c/a. For the given quadratic equation px² - 6x + 9 = 0, the sum of the roots (a + b) is a + b = -(-6)/p = 6/p. To find p² + q², we use the identity p² + q² = (p + q)² - 2pq where p + q = -b/a and pq = c/a, thus p² + q² = (b² - 4ac)/a².

For the equation 2x² - 5x + k = 0, the sum of roots (α+β) is α+β = -(-5)/2 = 5/2. An equation with roots x = 2 and x = -3 translates to (x - 2)(x + 3) = 0 or 2x² - 5x - 6 = 0. If b² - 4ac > 0, the quadratic equation has real and unequal roots.

If the discriminant (Δ) is zero, the roots are real and equal. The sum of the roots (α+β) of ax² + bx + c = 0 is α+β = -b/a. When the equation has no real roots, it means b² - 4ac < 0. The product of the roots (α •β) in terms of coefficients a, b, c is α •β = c/a.

Answer 2

1. b. mn = -c/a (by root-coefficient relationship)

2. a. a + b = 6/p (let the zeroes be x, and y, so x+y = -b/a)

3. b.
`(b^2 - 2ac)/(a^2)` (we can turn p^2 + q^2 to
`(p+q)^2 - 2pq`

4. c. k/2

5. d. x^2 - x - 6 = 0

6. a. The roots are real and unequal

7. b.

8. a.

9. c.

10. c.