Question

For which equation does the product of the roots equal 7/4 and the sum equal 9/4?

a) x²-2x+7/4=0
b) x²-3x+7/4=0
c) x²-4x+7/4=0
d) x²-2x+9/4=0

Answer 1

The equation that satisfies the given conditions is: x^2 - (9/4)x + 7/4 = 0 (Option b).

Step-by-step explanation:

Let's solve the problem using the quadratic formula.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

From the given information, we have:

Product of the roots = 7/4, which means that a*c = 7/4.

Sum of the roots = 9/4, which means that -b/a = 9/4.

Solving the equations:

a*c = 7/4, a = 1

-b/a = 9/4, b = -9/4

Therefore, the equation is: x^2 - (9/4)x + 7/4 = 0 (Option b).