KimDahDahyun
Answered

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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​

Sagot :

bigcrybaby

Answer: Solving quadratic inequalities involve writing quadratic inequality in standard form, finding its root, and write the solution in inequality notation form. A solution to a quadratic inequality is a real number that will produce a true statement when substituted for the variable.

Step-by-step explanation:

devishri1977

Answer:

Step-by-step 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

[tex]m=\dfrac{-b+\sqrt{D}}{2a} ; m = \dfrac{-b-sqrt{D}}{2a}\\\\\\m=\dfrac{-(-7)+\sqrt{89}}{2*1} \ ; \ m=\dfrac{-(-7)-\sqrt{89}}{2*1}\\\\\\m=\dfrac{7+9.43}{2} \ ; \ m=\dfrac{7-9.43}{2}\\\\m=\dfrac{16.43}{2} \ ; \ m=\dfrac{-2.43}{2}\\\\m=8.22 ; m = -1.21[/tex]

-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

View image devishri1977
View image devishri1977
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