The quadratic formula is used to solve for ???? in equations taking the form of a quadratic equation, ????????2+????????+????=0. quadratic formula:????=−????±√(????^2−4????????)/2????. Solve for ???? in the expression using the quadratic formula. 2????^2+31????−6.1=0. Use at least three significant figures in each answer.

Accepted Solution

Answer:Using the quadratic formula [tex]x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]The answer to the equation [tex]2x^{2} +31x-6.1=0[/tex] using at least three significant figures is:[tex]x_{1}=0.194\\x_{2}=-15.694[/tex]Step-by-step explanation:The quadratic formula is used to solve polynomials of second degree.We have a polynomial of second degree to be resolved with the quadratic formula:[tex]2x^{2} +31x-6.1=0[/tex] (Eq. 1)We know the quadratic formula is:[tex]x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex] (Eq. 2)To resolve the quadratic formula we need the a, b and c coefficients, we can find these coefficients in the equation 1.a: Coefficient that accompanies [tex]x^{2}[/tex]b: Coefficient that accompanies [tex]x[/tex]c: Independent termWith this information and the equation (1). We know the values of a, b and c[tex]a=2\\b=31\\c=-6.1\\[/tex]Now, we can replace these terms in the quadratic formula (Eq. 2)The first root will be found using the positive sign before the square root:[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex][tex]x=\frac{-31+\sqrt{31^{2}-[4*2*(-6.1)]} }{2*2}[/tex][tex]x=\frac{-31+\sqrt{961-(-48.8)} }{4}[/tex][tex]x=\frac{-31+\sqrt{961+48.8} }{4}[/tex][tex]x=\frac{-31+\sqrt{1009.8} }{4}[/tex][tex]x=\frac{-31+31.777 }{4}[/tex][tex]x=0.194[/tex]The second root will be found using the negative sign before the square root:[tex]x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex][tex]x=\frac{-31-\sqrt{31^{2}-[4*2*(-6.1)]} }{2*2}[/tex][tex]x=\frac{-31-\sqrt{961-(-48.8)} }{4}[/tex][tex]x=\frac{-31-\sqrt{961+48.8} }{4}[/tex][tex]x=\frac{-31-\sqrt{1009.8} }{4}[/tex][tex]x=\frac{-31-31.777 }{4}[/tex][tex]x=-15.694[/tex]