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Harder factorisation and rearranging
Optional extension. Rearrange equations and factorise ax² + bx + c, including fractional roots.
Example 1
4x2+8x−21=0
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Answer: x=23x=2−7
- To split the middle term, use 14 and −6: they add to 8 and multiply to a×c=−84.
- Factor by grouping: (2x−3)(2x+7)=0.
- Set each factor equal to zero: 2x=3 or 2x=−7.
- Therefore x=23 or x=2−7.
- Enter both roots, in either order.
Example 2
3x2+7x+2=0
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Answer: x=3−1x=−2
- To split the middle term, use 6 and 1: they add to 7 and multiply to a×c=6.
- Factor by grouping: (3x+1)(x+2)=0.
- Set each factor equal to zero: 3x=−1 or x=−2.
- Therefore x=3−1 or x=−2.
- Enter both roots, in either order.
Example 3
3x2−4x+1=0
Show worked answer
Answer: x=31x=1
- To split the middle term, use−3 and −1: they add to−4 and multiply to a×c=3.
- Factor by grouping: (3x−1)(x−1)=0.
- Set each factor equal to zero: 3x=1 or x=1.
- Therefore x=31 or x=1.
- Enter both roots, in either order.
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