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High School Math : Understanding the Discriminant

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Example Questions

Example Question #43 : Intermediate Single Variable Algebra

Use the discriminant to determine the nature of the roots:

$\displaystyle 4x^2-40x+25=0$

Possible Answers:

$\displaystyle 2$ rational roots

$\displaystyle 1$ imaginary root

$\displaystyle 2$ imaginary roots

$\displaystyle 2$ irrational roots

$\displaystyle 1$ rational root

Correct answer:

$\displaystyle 2$ irrational roots

Explanation:

The formula for the discriminant is:

$\displaystyle b^2 - 4ac$

$\displaystyle =(-40)^2 - 4(4)(25)$

$=1200^{}$ $\displaystyle =1200^{}$

Since the discriminant is positive and not a perfect square, there are $\displaystyle 2$ irrational roots.

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Example Question #12 : Quadratic Equations And Inequalities

Use the discriminant to determine the nature of the roots:

$\displaystyle 2y^2+6y+5=0$

Possible Answers:

$\displaystyle 1$ rational root

$\displaystyle 1$ imaginary root

$\displaystyle 2$ imaginary roots

$\displaystyle 2$ irrational roots

$\displaystyle 2$ rational roots

Correct answer:

$\displaystyle 2$ imaginary roots

Explanation:

The formula for the discriminant is:

$\displaystyle b^2 - 4ac$

$\displaystyle =(6)^2 - 4(2)(5)$

=-4 $\displaystyle =-4$

Since the discriminant is negative, there are $\displaystyle 2$ imaginary roots.

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Example Question #1 : Understanding The Discriminant

Use the discriminant to determine the nature of the roots:

$\displaystyle 4x^2-8x+13=0$

Possible Answers:

$\displaystyle 1$ imaginary root

Cannot be determined

$\displaystyle 2$ real roots

$\displaystyle 1$ real root

$\displaystyle 2$ imaginary roots

Correct answer:

$\displaystyle 2$ imaginary roots

Explanation:

The formula for the discriminant is:

$\displaystyle b^2 - 4ac$

$\displaystyle =(-8)^2 - 4(4)(13)$

=-144 $\displaystyle =-144$

Since the discriminant is negative, there are $\displaystyle 2$ imaginary roots.

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Example Question #1 : Discriminants

Given $2x^{2}+3x-5=0$ $\displaystyle 2x^{2}+3x-5=0$ , what is the value of the discriminant?

Possible Answers:

$\displaystyle 40$

$\displaystyle 27$

$\displaystyle 49$

$\displaystyle 7$

$\displaystyle -31$

Correct answer:

$\displaystyle 49$

Explanation:

In general, the discriminant is $b^{2}-4ac$ $\displaystyle b^{2}-4ac$.

In this particual case $a=2, b=3\; and\; c=-5$ $\displaystyle a=2, b=3\; and\; c=-5$.

Plug in these three values and simplify: $(3)^{2}-4(2)(-5)= 49$ $\displaystyle (3)^{2}-4(2)(-5)= 49$

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All High School Math Resources

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High School Math : Understanding the Discriminant

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #43 : Intermediate Single Variable Algebra

Example Question #12 : Quadratic Equations And Inequalities

Example Question #1 : Understanding The Discriminant

Example Question #1 : Discriminants

All High School Math Resources

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