Solve quadratic equations by factorisation and the quadratic formula, and determine the nature of roots using the discriminant.
Quadratic equations ax²+bx+c=0 can be solved by factorisation or the quadratic formula x=[-b±√(b²-4ac)]/2a.
Solve x²-6x+8=0 by factorisation.
(x-2)(x-4)=0; x=2 or x=4
Solve 2x²-5x+2=0 using the quadratic formula.
x=[5±√(25-16)]/4=[5±3]/4; x=2 or x=1/2
Solve x²+7x+10=0 by factorisation.
(x+2)(x+5)=0; x=−2 or x=−5
D=b²-4ac: if D>0, two distinct real roots; if D=0, equal real roots; if D<0, no real roots.
Find the discriminant of 2x²+3x+5=0 and describe the roots.
D=9-40=-31; no real roots
Find the discriminant of x²-4x+4=0 and describe the roots.
D=16-16=0; equal real roots
Find the discriminant of 4x²−4x+1=0 and describe the roots.
D=16−16=0; equal real roots
1. Solve x²-9x+20=0 by factorisation.
2. Solve x²+2x-8=0 by factorisation.
3. Solve x²-4x+1=0 using the quadratic formula.
4. Find the discriminant of 3x²-2x+1=0 and describe the roots.
5. Find k if x²-kx+9=0 has equal roots.
6. Solve x²+2x−15=0 by factorisation.
7. Solve x²−8x+15=0 by factorisation.
8. Solve using the formula: x²+3x−2=0
9. Find the discriminant of 3x²+2x+5=0 and describe the roots.
10. Find k if x²+kx+25=0 has equal roots.