KnowledgeBoat Logo

Mathematics

Solve the following equation by factorisation:

21x2 - 8x - 4 = 0

Quadratic Equations

27 Likes

Answer

Given,

21x28x4=021x214x+6x4=07x(3x2)+2(3x2)=0(7x+2)(3x2)=0 (Factorising left side) 7x+2=0 or 3x2=0 (Zero-product rule) x=27 or x=2321x^2 - 8x - 4 = 0 \\[0.5em] \Rightarrow 21x^2 - 14x + 6x - 4 = 0 \\[0.5em] \Rightarrow 7x(3x - 2) + 2(3x - 2) = 0 \\[0.5em] \Rightarrow (7x + 2)(3x - 2) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow 7x + 2 = 0 \text{ or } 3x - 2 = 0 \text{ (Zero-product rule) }\\[0.5em] \Rightarrow x = -\dfrac{2}{7} \text{ or } x = \dfrac{2}{3}

Hence, the roots of given equation are 27-\dfrac{2}{7}, 23\dfrac{2}{3}.

Answered By

18 Likes


Related Questions