Question

1. $4x^2 - 5x - 9 = 0$

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=4$, $b=-5$, $c=-9$

Step2: Calculate discriminant

$\Delta = b^2-4ac = (-5)^2 - 4(4)(-9) = 25 + 144 = 169$

Step3: Apply quadratic formula

$x = \frac{-b\pm\sqrt{\Delta}}{2a} = \frac{5\pm\sqrt{169}}{2(4)}$

Step4: Simplify to find roots

$x_1 = \frac{5+13}{8} = \frac{18}{8} = \frac{9}{4}$, $x_2 = \frac{5-13}{8} = \frac{-8}{8} = -1$

Answer:

$x = \frac{9}{4}$ or $x = -1$