Solve the following equation by factorisation:
3x2 - 5x - 12 = 0
Given,
3x2−5x−12=0⇒3x2−9x+4x−12=0⇒3x(x−3)+4(x−3)=0⇒(x−3)(3x+4)=0 (Factorising left side) ⇒x−3=0 or 3x+4=0 (Zero-product rule) ⇒x=3 or x=−433x^2 - 5x - 12 = 0 \\[0.5em] \Rightarrow 3x^2 - 9x + 4x - 12 = 0 \\[0.5em] \Rightarrow 3x(x - 3) + 4(x - 3) = 0 \\[0.5em] \Rightarrow (x - 3)(3x + 4) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow x - 3 = 0 \text{ or } 3x + 4 = 0 \text{ (Zero-product rule) }\\[0.5em] \Rightarrow x = 3 \text{ or } x = -\dfrac{4}{3}3x2−5x−12=0⇒3x2−9x+4x−12=0⇒3x(x−3)+4(x−3)=0⇒(x−3)(3x+4)=0 (Factorising left side) ⇒x−3=0 or 3x+4=0 (Zero-product rule) ⇒x=3 or x=−34
Hence, the roots of given equation are 3, −43-\dfrac{4}{3}−34.
Answered By
x2 - 3x - 10 = 0
x(2x + 5) = 3
21x2 - 8x - 4 = 0
3x2 = x + 4
