Understanding Quadratic Roots - Math

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Write an equation with the given roots:

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

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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:

Multiply the equation by :

Write an equation with the given roots:

$4 \pm $\sqrt{3}$$

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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:

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

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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:

Multiply the equation by :

Write an equation with the given roots:

$2 \pm $\sqrt{3}$$

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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:

$5 \pm 3i$

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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:

Write an equation with the given roots:

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

Tap to see back →

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:

Multiply the equation by :

Write an equation with the given roots:

$4 \pm $\sqrt{3}$$

Tap to see back →

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:

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

Tap to see back →

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:

Multiply the equation by :

Write an equation with the given roots:

$2 \pm $\sqrt{3}$$

Tap to see back →

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:

$5 \pm 3i$

Tap to see back →

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:

Write an equation with the given roots:

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

Tap to see back →

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:

Multiply the equation by :

Write an equation with the given roots:

$4 \pm $\sqrt{3}$$

Tap to see back →

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:

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

Tap to see back →

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:

Multiply the equation by :

Write an equation with the given roots:

$2 \pm $\sqrt{3}$$

Tap to see back →

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:

$5 \pm 3i$

Tap to see back →

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:

Write an equation with the given roots:

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

Tap to see back →

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:

Multiply the equation by :

Write an equation with the given roots:

$4 \pm $\sqrt{3}$$

Tap to see back →

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:

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

Tap to see back →

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:

Multiply the equation by :

Write an equation with the given roots:

$2 \pm $\sqrt{3}$$

Tap to see back →

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:

$5 \pm 3i$

Tap to see back →

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: