Understanding Quadratic Roots

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Math › Understanding Quadratic Roots

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Write an equation with the given roots:

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

CORRECT

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 :

Write an equation with the given roots:

$4 \pm \sqrt{3}$

CORRECT

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:

Write an equation with the given roots:

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

CORRECT

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 :

Write an equation with the given roots:

$2 \pm \sqrt{3}$

CORRECT

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:

Write an equation with the given roots:

$5 \pm 3i$

CORRECT

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:

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

Subtract the sum and add the product.

The equation is:

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