Question

Find The Solution set and draw a number line of each quad inequality

1. x²-x+2≤ 0
3. x² + 9x + 18 < 0
4. m²- 7m < 10
5. 2x²- 3x - 14 < 0​

Answer 1

Explanation:

1) x² - x + 2 ≤ 0

x² -x - x + 2 ≤0

x(x - 1) - (x - 1) ≤ 0

(x - 1)(x - 1) ≤0

No solution

3) x² + 9x + 18 < 0

x² + 6x + 3x + 18 < 0

x(x + 6) +3(x + 6) < 0

(x + 6)(x + 3) < 0

x > - 6; x < -3

-6 < x < -3

4) m² - 7m - 10 < 0

a = 1 ; b = -7 c = -10

D = b² - 4ac = (-7)² - 4*1*(-10) = 49 + 40 = 89

`m=(-b+√(D))/(2a) ; m = \frac{-b-sqrt{D}}{2a}\\\\\\m=(-(-7)+√(89))/(2*1) \ ; \ m=(-(-7)-√(89))/(2*1)\\\\\\m=(7+9.43)/(2) \ ; \ m=(7-9.43)/(2)\\\\m=(16.43)/(2) \ ; \ m=(-2.43)/(2)\\\\m=8.22 ; m = -1.21`

-1.21 < m < 8.22

-1 < m < 8

5) 2x² - 3x - 14 < 0

2x² + 4x - 7x - 14 < 0

2x(x + 2) - 7(x + 2) < 0

(x + 2)(2x -7) < 0

-2 < x < 7/2

-2 < x < 3.5