Question

What are the approximate solutions of 4x^2 + 3 = -12x to the nearest hundredth?

A.) x ≈ -3.23 and x ≈ 0.23
B.) x ≈ -2.72 and x ≈ -0.28
C.) x ≈ 0.28 and x ≈ 2.72
D.) x ≈ -0.23 and x ≈ 3.23

Answer 1

add 12x to both sides
4x^2+12x+3=0
we cannot factor
use quadractic formula
for an eqution
ax^2+bx+c=0
x=$\frac{-b+/- \sqrt{b^2-4ac} }{2a}$

a=4
b=12
c=3
x=$\frac{-12+/- \sqrt{12^2-4(4)(3)} }{2(4)}$
x=$\frac{-12+/- \sqrt{144-48} }{8}$
x=$\frac{-12+/- \sqrt{96} }{8}$
x=$\frac{-12+/- 4\sqrt{6} }{8}$
x=$\frac{-3+/- \sqrt{6} }{2}$
aprox
x=-2.7247 or -0.2752

B is answer

Answer 2

Approximate solution of quadratic equation 4x² +3 = -12x is x ≈-2.72 and x ≈ -0.28.

What is Quadratic equation?

" Quadratic equation is an algebraic equation whose highest degree is two with 'a' as coefficient. General form of quadratic equation is

ax² + bx +c=0."

Formula used

General form : ax² + bx +c =0

x = (-b ±√b² -4ac)/2a

According to the question,

4x² +12x +3=0

a=4 , b=12 , c = 3

x = [-12 ±√12² -4(4)(3)]/2(4)

  = (-12 ±√6)/8

 ⇒ x=(-3+√6)/2 or x= (-3-√6)/2

⇒x = -0.2752  or x= -2.7247

⇒ x≈ -0.28 or x ≈-2.72 (nearest hundredth)

Hence, Approximate solution of quadratic equation 4x² +3 = -12x is x ≈-2.72 and x ≈ -0.28.

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