Solving Equations (Leaving Cert Mathematics): Quizzes

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Quadratic Equations with Complex Roots
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What method is used to solve quadratic equations with complex roots?

Quadratic formula

What is the standard form of a quadratic equation as shown in the note?

az2+bz+c=0az^2+bz+c=0

What causes a quadratic equation to have complex roots?

Negative number under square root

Why can't calculators find roots of quadratics with complex roots directly?

Error from negative under square root

In 2z2+10z+13=02z^2+10z+13=0, what is the value of coefficient aa?

22

For 2z2+10z+13=02z^2+10z+13=0, what is b2−4acb^2-4ac?

−4-4

What is −4\sqrt{-4} equal to in terms of ii?

2i2i

How do complex roots of a quadratic equation appear?

In conjugate pairs

What must be done manually for quadratics with complex roots?

The calculations

For 2z2+10z+13=02z^2+10z+13=0, what is the real part of the roots?

−52-\frac{5}{2}

What is the discriminant in a quadratic equation?

b2−4acb^2 - 4ac

When do complex roots occur in a quadratic equation?

When b2−4ac<0b^2 - 4ac < 0

What is the value of i2i^2?

−1-1

What is the quadratic formula for ax2+bx+c=0ax^2+bx+c=0?

x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

In 2x2+10x+13=02x^2+10x+13=0, what is the value of aa?

22

Why must students show full working when finding complex roots?

For exam marks

What is the standard form of a quadratic equation?

ax2+bx+c=0ax^2+bx+c=0

For 2x2+10x+13=02x^2+10x+13=0, what is b2−4acb^2-4ac?

−4-4

What type of roots result from a negative discriminant?

Complex roots

In 2x2+10x+13=02x^2+10x+13=0, what is the value of cc?

1313

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