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高中数学:Understanding Quadratic Roots

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Example Questions

Example Question #13 :Quadratic Equations And Inequalities

Write an equation with the given roots:

$\frac{3}{4}, \frac{1}{3}$

Possible Answers:

12x^2-13x+3=0

13x^2-12x+3=0

14x^2-13x+3=0

13x^2-13x+3=0

13x^2-12x+2=0

Correct answer:

12x^2-13x+3=0

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of, and the product is the integer.

Sum: $(\frac{3}{4})+(\frac{1}{3})=\frac{13}{12}$

Product: $(\frac{3}{4})\cdot (\frac{1}{3})=\frac{1}{4}$

Subtract the sum and add the product.

The equation is:

$x^2 - \frac{13}{12}x+\frac{1}{4}=0$

Multiply the equation by:

12x^2+-13x+3=0

Report an Error

Example Question #14 :Quadratic Equations And Inequalities

Write an equation with the given roots:

$2 \pm \sqrt{3}$

Possible Answers:

x^2-3x+1=0

x^2-2x+2=0

x^2-3x+2=0

x^2-4x+1=0

x^2-4x+2=0

Correct answer:

x^2-4x+1=0

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of, and the product is the integer.

Sum: $(2 + \sqrt{3})+(2 - \sqrt{3})=4$

Product: $(2 + \sqrt{3})\cdot (2 - \sqrt{3})=4-3=1$

Subtract the sum and add the product.

The equation is:

x^2 -4x+1=0

Report an Error

Example Question #21 :Quadratic Equations And Inequalities

Write an equation with the given roots:

$5 \pm 3i$

Possible Answers:

x^2-10x+14=0

x^2-10x+34=0

x^2-10x+24=0

x^2-8x+34=0

x^2-8x+24=0

Correct answer:

x^2-10x+34=0

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of, and the product is the integer.

Sum: (5 + 3i)+(5-3i)=10

Product: $(5+3i)\cdot (5-3i)=25-9i^2=34$

Subtract the sum and add the product.

The equation is:

x^2-10x+34=0

Report an Error

Example Question #22 :Quadratic Equations And Inequalities

Write an equation with the given roots:

$-\frac{3}{5}, \frac{1}{2}$

Possible Answers:

9x^2+x-3=0

8x^2+x-3=0

11x^2+x-3=0

7x^2+x-3=0

10x^2+x-3=0

Correct answer:

10x^2+x-3=0

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of, and the product is the integer.

Sum: $(\frac{-3}{5})+(\frac{1}{2})=\frac{-1}{10}$

Product: $(\frac{-3}{5})\cdot (\frac{1}{2})=\frac{-3}{10}$

Subtract the sum and add the product.

The equation is:

$x^2 + \frac{1}{10}x-\frac{3}{10}=0$

Multiply the equation by:

10x^2+x-3=0

Report an Error

Example Question #1 :Understanding Quadratic Roots

Write an equation with the given roots:

$4 \pm \sqrt{3}$

Possible Answers:

x^2-9x+13=0

x^2-8x+12=0

2x^2-9x+13=0

x^2-8x+13=0

x^2-7x+13=0

Correct answer:

x^2-8x+13=0

Explanation:

To write an equation, find the sum and product of the roots. The sum is the negative coefficient of, and the product is the integer.

Sum: $(4 + \sqrt{3})+(4 - \sqrt{3})=8$

Product: $(4 + \sqrt{3})\cdot (4 - \sqrt{3})=16-3=13$

Subtract the sum and add the product.

The equation is:

x^2 -8x+13=0

Report an Error

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高中数学:Understanding Quadratic Roots

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #13 :Quadratic Equations And Inequalities

Example Question #14 :Quadratic Equations And Inequalities

Example Question #21 :Quadratic Equations And Inequalities

Example Question #22 :Quadratic Equations And Inequalities

Example Question #1 :Understanding Quadratic Roots

All High School Math Resources

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