ic equations Flashcards","topicId":"2343ca6c-e772-4b6a-9322-a17e61e3b369","topicSlug":"solve-quadratic-equations","cards":[{"id":"80964fe3-8848-43aa-a967-38db57eb7f91","cardType":"basic","front":"Why must $a\\neq 0$ in $ax^2+bx+c=0$?","back":"If $a=0$, the equation is linear, not quadratic.","points":2,"mcqOptions":null},{"id":"0c2ff85b-b2d1-44ad-b352-24035c20cbc7","cardType":"cloze","front":"Before factorising a quadratic, rearrange it so that one side equals $\\text{[...]}$.","back":"Before factorising a quadratic, rearrange it so that one side equals $\\boxed{0}$.","points":null,"mcqOptions":null},{"id":"30bf978a-01fa-4457-8563-b93fffe2b978","cardType":"basic","front":"What rule allows $(x-2)(x+3)=0$ to be split into two linear equations?","back":"The zero-product rule.","points":1,"mcqOptions":null},{"id":"a91e5eaf-f134-478d-973d-aecc2895ae39","cardType":"basic","front":"Why can the zero-product rule not be applied directly to $(x-2)(x+3)=5$?","back":"The product does not equal zero.","points":2,"mcqOptions":null},{"id":"ce7a7f64-432a-4cb1-9770-c716fe1acaff","cardType":"basic","front":"For $x^2+bx+c$, what conditions must the two factorising numbers satisfy?","back":"

Product: $c$
Sum: $b$

","points":3,"mcqOptions":null},{"id":"0bf76435-f299-45fd-81e7-9c6d42a555fd","cardType":"basic","front":"Solve $x^2-7x+12=0$.","back":"$x=3$ or $x=4$.","points":2,"mcqOptions":null},{"id":"e9078d35-155d-4777-87dd-6c329b02d105","cardType":"basic","front":"Solve $6x^2+x-2=0$.","back":"$x=\\frac12$ or $x=-\\frac23$.","points":2,"mcqOptions":null},{"id":"429fb713-7472-4892-b9ac-16ca600db690","cardType":"cloze","front":"When $u^2=q$ and $q>0$, taking square roots gives $\\text{[...]}$.","back":"When $u^2=q$ and $q>0$, taking square roots gives $\\boxed{u=\\pm\\sqrt q}$.","points":null,"mcqOptions":null},{"id":"3e0aede8-f7df-4c57-aaa4-6d3ec1beaf37","cardType":"basic","front":"Solve $3(x-2)^2=15$.","back":"$x=2\\pm\\sqrt5$.","points":2,"mcqOptions":null},{"id":"b1322e10-265b-4c97-b583-f8f5b853a2a8","cardType":"basic","front":"Rewrite $x^2+6x+2$ in completed-square form.","back":"$(x+3)^2-7$.","points":2,"mcqOptions":null},{"id":"86fe7beb-3a39-4724-a1d1-61603796599e","cardType":"basic","front":"Solve $x^2+6x+2=0$ by completing the square.","back":"$x=-3\\pm\\sqrt7$.","points":2,"mcqOptions":null},{"id":"131738c0-a412-488b-864c-eb721e9a1310","cardType":"basic","front":"What turning point does $y=(x+3)^2-7$ have?","back":"$(-3,-7)$.","points":2,"mcqOptions":null},{"id":"496276a0-652f-40fa-b6dd-c8b61036c374","cardType":"cloze","front":"For $ax^2+bx+c=0$, the quadratic formula is $\\text{[...]}$.","back":"For $ax^2+bx+c=0$, the quadratic formula is $\\boxed{x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}}$.","points":null,"mcqOptions":null},{"id":"f9602782-4b73-4cb0-b6ed-30b672274cb1","cardType":"basic","front":"Why should a negative coefficient such as $b=-3$ be bracketed when substituted into $b^2$?","back":"It ensures $(-3)^2=9$, avoiding interpretation as $-(3^2)$.","points":2,"mcqOptions":null},{"id":"b9050d0a-a83f-4555-9a9c-0989558ec64a","cardType":"basic","front":"Solve $2x^2-3x-4=0$, giving exact answers.","back":"$x=\\frac{3\\pm\\sqrt{41}}4$.","points":2,"mcqOptions":null},{"id":"e9302b00-9741-40e2-bdef-34e23b7d15d6","cardType":"cloze","front":"For $ax^2+bx+c=0$, the discriminant is $\\text{[...]}$.","back":"For $ax^2+bx+c=0$, the discriminant is $\\boxed{\\Delta=b^2-4ac}$.","points":null,"mcqOptions":null},{"id":"4ca72d93-3d2d-4d7e-af0a-aa1c9b45219f","cardType":"basic","front":"What does $\\Delta>0$ imply about the roots?","back":"There are two distinct real roots.","points":1,"mcqOptions":null},{"id":"c33579f3-8189-4e5c-bf9f-d99f7217cf9c","cardType":"basic","front":"What does $\\Delta=0$ imply about the roots and graph?","back":"The graph touches the $x$-axis at one repe

1.2.4 Solve quadratic equations Flashcards

1.2.4 Solve quadratic equations Flashcards