Solving-Quadratics-By-Factorising Aqa Higher

Solving quadratics by factorising

How do I solve a quadratic equation using factorisation?

• Rearrange it into the form ax² + bx + c = 0

  • Zero must be on one side

  • It is easier if you rearrange so that a is positive

• Factorise the quadratic and solve each bracket equal to zero

  • If (x + 4)(x – 1) = 0, then either x + 4 = 0 or x – 1 = 0

    • Because if two things multiply together to give zero,

      • then one or the other of them must be equal to zero

• To solve

  • …solve first bracket = 0:

    • x – 3 = 0 

    • add 3 to both sides: x = 3

  • …and solve second bracket = 0

    • x + 7 = 0

    • subtract 7 from both sides: x = -7

  • The two solutions are x = 3 or x = -7

    • The solutions in this example are the numbers in the brackets, but with opposite signs

What if there are numbers in front of the x’s in the brackets?

• The process is the same

  • There’s a bit more work to find the solutions

  • You can’t just write down the answers by changing the signs

• To solve 

  • …solve first bracket = 0

    • 2x – 3 = 0

    • add 3 to both sides: 2x = 3

    • divide both sides by 2: x = 

  • …solve second bracket = 0

    • 3x + 5 = 0

    • subtract 5 from both sides: 3x = -5

    • divide both sides by 3: x = 

  • The two solutions are x =  or x = <img alt=”negative 5 over 3″ data-mathml='<math ><semantics><mrow><mo>-</mo><mfrac><mn>5</mn><mn>3</mn></mfrac></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”47″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2247%22%20width%3D%2231%22%20wrs%3Abaseline%3D%2230%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E5%3C%2Fmn%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1da40657c9fece7e48d30af42d3’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAcmhlYWQQC2qxAAACAAAAADZoaGVhCGsXSAAAAjgAAAAkaG10eE2rRkcAAAJcAAAACGxvY2EAHTwYAAACZAAAAAxtYXhwBT0FPgAAAnAAAAAgbmFtZaBxlY4AAAKQAAABn3Bvc3QB9wD6AAAEMAAAACBwc