The value of r - s from the solutions of the quadratic equation is 6.5.
The given equation;
2x² + 7x - 15 = 0
The two solutions of the given quadratic equation is obtained by solving the equation using formula method as shown below;
a = 2, b = 7, c = -15
[tex]x = \frac{-b \ \ +/- \ \ \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-7 \ \ + /- \ \ \sqrt{(7)^ - 4(2\times -15)} }{2(2)} \\\\x= \frac{-7 \ \ +/- \ \sqrt{169} }{4} \\\\x = \frac{-7 \ \ +/- \ \ 13}{4} \\\\x = 1.5 \ \ \ or \ \ -5[/tex]
Since r > s
r = 1.5 and s = -5
Then, r - s = 1.5 - (-5) = 1.5 + 5 = 6.5
Thus, the value of r - s from the solutions of the quadratic equation is 6.5.
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