4. If the solution of 2x² + (k- 3) x - 7 = 0are 3.5 and -1,then what is the value of k?

1 answer

In a quadratic equation of the form ax² + bx + c = 0, the sum of the solutions is given by the formula: x₁ + x₂ = -b/a

In this case, the sum of the solutions is:

3.5 + (-1) = -b/a

Simplifying:

2.5 = -b/a

On the other hand, the product of the solutions is given by the formula: x₁ * x₂ = c/a

In this case, the product of the solutions is:

3.5 * (-1) = -7/2

Simplifying:

-3.5 = -7/2

To find the value of k, we need to find the value of b. By comparing the coefficients of the quadratic equation, we can deduce that b = k - 3.

Substituting b = k - 3 into the equation -b/a = 2.5:

- (k - 3)/a = 2.5

Cross-multiplying:

-2.5a = k - 3

Simplifying:

k = -2.5a + 3

Now, using the equation -3.5 = -7/2:

-3.5 = -7/2

Multiplying both sides by 2:

-7 = -14/2

Simplifying:

-7 = -7

This equation is true for any value of a. Therefore, we can let a = 1. Substituting a = 1 into the equation k = -2.5a + 3:

k = -2.5(1) + 3

Simplifying:

k = -2.5 + 3

k = 0.5

Thus, the value of k is 0.5.