6. Complete the table below. The first one has been done for you.
For each statement you must state if it is always true, sometimes true or never true, giving a reason in each case.
| Statement | Always True | Sometimes True | Never True | Reason |
| The quadratic equation \(a x ^ { 2 } + b x + c = 0 , \quad ( a \neq 0 )\) has 2 real roots. | | ✓ | | It only has 2 real roots when \(b ^ { 2 } - 4 a c > 0\). When \(b ^ { 2 } - 4 a c = 0\) it has 1 real root and when \(b ^ { 2 } - 4 a c < 0\) it has 0 real roots. |
| (i) | | When a real value of \(x\) is substituted into \(x ^ { 2 } - 6 x + 10\) the result is positive. |
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| (ii) | | If \(a x > b\) then \(x > \frac { b } { a }\) | | (2) |
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| (iii) | | The difference between consecutive square numbers is odd. |
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