Question

solve the following equation by factorization 4x²-12x+45=0​

Answer 1

Step-by-step explanation:

$\tt \implies4x ^ { 2 } -12x+45=0$

$\tt \implies \: x ^ 2 -3x +\dfrac{45}{4} = 0$

$\tt \implies \: r + s = 3 \\ \tt rs = \frac{45}{4}$

$\tt\implies \: r = \frac{3}{2} - u \\ \tt s = \frac{3}{2} + u$

$\tt \implies \left(\dfrac{3}{2} - u \right) \left(\dfrac{3}{2} + u \right) = \dfrac{45}{4}$

$\tt \implies\dfrac{9}{4} - u^2 = \dfrac{45}{4}$

$\tt \implies-u^2 = \dfrac{45}{4}-\dfrac{9}{4} = 9$

$\tt\implies \: u^2 = -9 u = \pm\sqrt{-9} = \pm 3i$

$\tt\implies r =\dfrac{3}{2} - 3i \\ \tt \: s = \dfrac{3}{2} + 3i$

$\rule{500pt}{5pt}$