Question

question 17 (mandatory) (1 point) saved
determine the roots of $3.3x^2 + 1.9x - 2.4 = 0$ to the nearest hundredth.

a) 1.19

b) -1.19 and 0.61

c) no real solution

d) -0.61 and 1.19

Explanation:

Step1: Recall Quadratic Formula

For \(ax^2 + bx + c = 0\), roots are \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 3.3\), \(b = 1.9\), \(c=-2.4\).

Step2: Calculate Discriminant

\(D=b^2 - 4ac=(1.9)^2-4(3.3)(-2.4)=3.61 + 31.68 = 35.29\).

Step3: Find Roots

\(x=\frac{-1.9\pm\sqrt{35.29}}{2(3.3)}=\frac{-1.9\pm5.94}{6.6}\).
First root: \(\frac{-1.9 + 5.94}{6.6}=\frac{4.04}{6.6}\approx0.61\).
Second root: \(\frac{-1.9 - 5.94}{6.6}=\frac{-7.84}{6.6}\approx - 1.19\).

Answer:

b) -1.19 and 0.61