Easy -1.2 This is a straightforward application of the discriminant formula b²-4ac with simple arithmetic (25-24=1), followed by direct recall that positive discriminant means two distinct real roots. No problem-solving required, just routine procedure with small numbers.
allow seen in formula; need not have numbers substituted but discriminant part must be correct
1 www
A1
clearly found as discriminant, or stated as \(b^2 - 4ac\), not just seen in formula eg M1A0 for \(\sqrt{b^2 - 4ac} = \sqrt{1} = 1\)
2 [distinct real roots]
B1
B0 for finding the roots but not saying how many there are
$b^2 - 4ac$ soi | M1 | allow seen in formula; need not have numbers substituted but discriminant part must be correct
1 www | A1 | clearly found as discriminant, or stated as $b^2 - 4ac$, not just seen in formula eg M1A0 for $\sqrt{b^2 - 4ac} = \sqrt{1} = 1$
2 [distinct real roots] | B1 | B0 for finding the roots but not saying how many there are | condone discriminant not used; ignore incorrect roots found
Find the discriminant of $3x^2 + 5x + 2$. Hence state the number of distinct real roots of the equation $3x^2 + 5x + 2 = 0$. [3]
\hfill \mbox{\textit{OCR MEI C1 2011 Q7 [3]}}