Solve by factorisation. 3x^2 + 11x – 20 = 0
Factorisation is a skill learned through a lot of practise. For questions with a coefficient of x, I like to use the 'House Method'.Step 1 - multiply the coefficient of x2 with the constant. =3*(-20)=-60Step 2 - Write out factors of this multiple which sum to the coefficient of x.=1 and 60 (can't make 11)=2 and 30 (can't make 11)=3 and 20 (can't make 11)=4 and 15 (15-4=11)Step 3 - Split the 'x' term into the two factors. =3x2+15x-4x-20 (notice that 3 & 15 and 4 & 20 have common factors, hence why I chose to put 15x-4x instead of -4x+15x)Step 4 - Split the equation into two and factorise. You should get the same terms in the brackets for both 'sides' of the equation. =3x2+15x = 3x(x+5)=-4x-20 = -4(x+5)Step 5 - The fully factorised form of the equation is the common bracket times the remaining terms=(x+5)(3x-4)Step 5 - Determine values of x by putting each bracket equal to 0x+5=0 therefore x=-53x-4=0 therefore x=4/3
