Question

2x^2 + 7x - 15 = 0If r and s are two solutions of the equation above and r>s, which of the following is the value of r - s?

Answer 1

Given:

The equation is given as,

`2x^2+7x-15=0`

The solutions of the above equation are r and s.

The objective is to find r - s.

Step-by-step explanation:

From the quadratic equation consider a = 2, b = 7 and c = -15.

The solutions r and s can be calculated using quadratic formula as,

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Substitute the value of a, b and c in the above formula.

`\begin{gathered} x=\frac{-7\pm\sqrt[]{7^2-4(2)(-15)}}{2(2)} \\ =\frac{-7\pm\sqrt[]{49+120}}{4} \\ =\frac{-7\pm\sqrt[]{169}}{4} \\ =(-7\pm13)/(4) \end{gathered}`

To find r and s:

On further solving the equation,

`\begin{gathered} x=(-7+13)/(4),(-7-13)/(4) \\ =(6)/(4),(-20)/(4) \\ =(3)/(2),-5 \end{gathered}`

Since, it is given that r > s, the value of r is (3/2) and s is -5.

To find r - s:

Now, the difference can be calcualted as,

`\begin{gathered} r-s=(3)/(2)-(-5) \\ =(3)/(2)+5 \\ =(3)/(2)+(5(2))/(2) \\ =(3)/(2)+(10)/(2) \\ =(13)/(2) \end{gathered}`

Thus, the value of r - s is (13/2).

Hence, option (B) is the correct answer.