Question

14) Solve the following quadratic equations by using the quadratic formula a) 3x2 - 7x + 4 = 0 b) 5x2 + 3x = 9

Answer 1

Quadratic formula

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

Where a is the coefficient of the first term, b the coefficient of the second term and c the coefficient of third term

a)

`3x^2-7x+4=0`

replacing on the quadratic formula

`x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(3)(4)}}{2(3)}`

simplify

`\begin{gathered} x=\frac{7\pm\sqrt[]{49-48}}{6} \\ \\ x=\frac{7\pm\sqrt[]{1}}{6} \\ \\ x=(7\pm1)/(6) \end{gathered}`

x has two solutions

`\begin{gathered} x_1=(7+1)/(6)=(4)/(3) \\ \\ x_2=(7-1)/(6)=1 \end{gathered}`

b)

`5x^2+3x=9`

rewrite on general form

`5x^2+3x-9=0`

raplace on quadratic formula

`x=\frac{-(3)\pm\sqrt[]{(3)^2-4(5)(-9)}}{2(5)}`

simplify

`\begin{gathered} x=\frac{-3\pm\sqrt[]{9+180}}{10} \\ \\ x=\frac{-3\pm\sqrt[]{189}}{10} \end{gathered}`

x has two solutions

`\begin{gathered} x_1=\frac{-3+\sqrt[]{189}}{10}\approx1.075 \\ \\ x_2=\frac{-3-\sqrt[]{189}}{10}\approx-1.67 \end{gathered}`