Question

d. $4x^2 + 4x - 3 = 0$

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=4$, $b=4$, $c=-3$

Step2: Calculate discriminant

$\Delta = b^2-4ac = 4^2 - 4(4)(-3) = 16 + 48 = 64$

Step3: Apply quadratic formula

$x = \frac{-b\pm\sqrt{\Delta}}{2a} = \frac{-4\pm\sqrt{64}}{2(4)}$

Step4: Simplify to find roots

First root: $x = \frac{-4+8}{8} = \frac{4}{8} = \frac{1}{2}$
Second root: $x = \frac{-4-8}{8} = \frac{-12}{8} = -\frac{3}{2}$

Answer:

$x=\frac{1}{2}$ and $x=-\frac{3}{2}$