Quadratic Equations (Leaving Cert Mathematics): Quizzes

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Using the Quadratic Formula
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When is the quadratic formula particularly useful?

When factorisation isn't possible

In the standard form ax2+bx+c=0ax^2 + bx + c = 0, what must be true about aa?

a≠0a ≠ 0

For 5x2+7x−3=05x^2 + 7x - 3 = 0, what are the values of aa, bb, and cc?

a=5a=5, b=7b=7, c=−3c=-3

What does the ± symbol in the quadratic formula represent?

Two possible solutions

If b2−4ac>0b^2 - 4ac > 0, what does this tell us about the solutions?

Two different real solutions

What type of solution exists when b2−4ac=0b^2 - 4ac = 0?

One repeated real solution

If b2−4ac<0b^2 - 4ac < 0, what can we conclude?

No real solutions

For 5x2+7x−3=05x^2 + 7x - 3 = 0, what is the value of b2−4acb^2 - 4ac?

109109

What is the first step in using the quadratic formula?

Identify the coefficients

In the rectangle area problem, why is only the positive solution used?

Length cannot be negative

What should you be particularly careful with when using the formula?

Negative coefficients

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