Solve the following equation by factorisation:
21x2 - 8x - 4 = 0
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Given,
21x2−8x−4=0⇒21x2−14x+6x−4=0⇒7x(3x−2)+2(3x−2)=0⇒(7x+2)(3x−2)=0 (Factorising left side) ⇒7x+2=0 or 3x−2=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}21x2−8x−4=0⇒21x2−14x+6x−4=0⇒7x(3x−2)+2(3x−2)=0⇒(7x+2)(3x−2)=0 (Factorising left side) ⇒7x+2=0 or 3x−2=0 (Zero-product rule) ⇒x=−72 or x=32
Hence, the roots of given equation are −27-\dfrac{2}{7}−72, 23\dfrac{2}{3}32.
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x(2x + 5) = 3
3x2 - 5x - 12 = 0
3x2 = x + 4
x(6x - 1) = 35
