Explanation Given: The given inequality is 2 x 2 + 3 x ≥ 27 . Formula used: Quadratic formula: The root of the quadratic equation a x 2 + b x + c = 0 is given by; x = − b ± b 2 − 4 a c 2 a Calculation: Consider the provided inequality 2 x 2 + 3 x ≥ 27 ; Solve the given inequality as: 2 x 2 + 3 x − 27 ≥ 0 Now, to calculate the boundary point, solve the equation 2 x 2 + 3 x − 27 = 0 ; Quadratic formula: The root of the quadratic equation a x 2 + b x + c = 0 is given by; x = − b ± b 2 − 4 a c 2 a Compare the equation 2 x 2 + 3 x − 27 = 0 with the general form a x 2 + b x + c = 0 to get; a = 2 , b = 3 and c = − 27 Use the quadratic formula to find the boundary points as: x = − ( 3 ) ± ( 3 ) 2 − 4 ( 2 ) ( − 27 ) 2 ( 2 ) = − 3 ± 9 + 216 4 = − 3 ± 225 4 = − 3 ± 15 4 Now, find the nearest possible boundary of x as: x = − 3 + 15 4 = 3 And, x = − 3 − 15 4 = − 9 2 Divide the number line with the help of this boundary points

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ISBN: 9780135909942

Author: TOBEY/SLATER

Publisher: PEARSON

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Chapter 8, Problem 18T

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To calculate: The solution of the given quadratic inequalities 2x2+3x≥27.

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Chapter 8, Problem 17T

Chapter 8, Problem 19T

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The solution of the given quadratic inequalities 2 x 2 + 3 x ≥ 27 .

Solution Summary: The author explains the quadratic equation ax2+bx+c=0 to calculate the boundary point.

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