Question

2. Given that ∝ and β are the roots of an equation such that ∝ +β = 3 and αβ =

1, Find the equation
A. x^2 − 3x + 2 = 0
B. x^2 − 2x + 3 = 0
C. x^2 − 3x − 2 = 0
D. x^2 − 2x − 3 = 0
2. If the equation x^2 − x + p = 0 has coincidental roots, find the value of P
A. −1÷2
B. 1÷4
C. 1÷2
D. 1
3. Find without necessarily solving the equation, the nature of the roots of the
equation 3x^2 − x + 3 = 0
A. Distinct two roots.
B. Complex roots
C. Coincident real roots
D. None
4. Find the sum of the equation in 20^2 − 40 = 120
A. 2
B. -2
C. 4
D. -4

Answer 1

1. (not enough info).

2. p =1/4.

3. B. Complex roots.

4. A. 2.

Explanation:

1. You have not wrote what αβ is.

As ∝ +β = 3 = -b/a the correct choice is either A or C.

2. p will have to be a square number

and -√p + -√p must be -1.

so p must be 1/4.

x^2 - 1x + 1/4 = (x - 1/2)(x - 1/2) and the coincidental roots are 1/2.

3. 3x^2 − x + 3 = 0

Work out the discriminant D (b^2 - 4ac).

D = (-1)^2 - 4*3*3 = -35

D is negative so the roots are complex.

4. I am assuming you mean the sum of the roots in equation

20x^2 - 40x = 120

Sum of roots = -b/a

= -(-40)/ 20

= 40/20

= 2.