What is the sum of the two solutions to the quadratic equation 2x^2 - 7x - 4 = 0? — ACT

What is the sum of the two solutions to the quadratic equation $2x^2 - 7x - 4 = 0$ ?

Cevap: 3.5

The sum of the solutions is

3.5

The sum of the solutions of the quadratic equation

2x^2 - 7x - 4 = 0

3.5

. According to Vieta's formulas, the sum of the roots of a quadratic equation in the form

ax^2 + bx + c = 0

is given by

-\frac{b}{a}

. Here,

a = 2

and

b = -7

, so the sum is

-\frac{-7}{2} = 3.5

. Alternatively, solving the equation using the quadratic formula yields the roots

4

and

-0.5

, which sum to

3.5

Identify the coefficients from the quadratic equation

2x^2 - 7x - 4 = 0

a = 2

b = -7

, and

c = -4

A quadratic equation in standard form is written as

ax^2 + bx + c = 0

Apply the sum of roots formula

-\frac{b}{a}

Sum

= -\frac{-7}{2} = 3.5

By Vieta's formulas, the sum of the roots of

ax^2 + bx + c = 0

-\frac{b}{a}

Sum of roots of a quadratic equation using Vieta's formulas

Solve the quadratic equation by factoring or using the quadratic formula. Factoring

2x^2 - 7x - 4 = 0

yields

(2x + 1)(x - 4) = 0

, which gives solutions

x = -0.5

and

x = 4

. Adding these solutions together gives

-0.5 + 4 = 3.5

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