Solve p^2-2p-9 - ScanMath

Question

Find the roots

p_{1} = 1 - 10, p_{2} = 1 + 10

Alternative Form

p_{1} \approx - 2.162278, p_{2} \approx 4.162278

Evaluate

p^{2} - 2 p - 9

To find the roots of the expression,set the expression equal to 0

p^{2} - 2 p - 9 = 0

Substitute a= 1,b= - 2 and c= - 9 into the quadratic formula p = \frac{- b \pm b ^{2} - 4 a c}{2 a}

p = \frac{2 \pm ( - 2 ) ^{2} - 4 ( - 9 )}{2}

Simplify the expression

More Steps

Evaluate

(- 2)^{2} - 4 (- 9)

Multiply the numbers

More Steps

Evaluate

4 (- 9)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 9

Multiply the numbers

- 36

(- 2)^{2} - (- 36)

Rewrite the expression

2^{2} - (- 36)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2^{2} + 36

Evaluate the power

4 + 36

Add the numbers

40

p = \frac{2 \pm 40}{2}

Simplify the radical expression

More Steps

Evaluate

40

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 10

Write the number in exponential form with the base of 2

2^{2} \times 10

The root of a product is equal to the product of the roots of each factor

2^{2} \times 10

Reduce the index of the radical and exponent with 2

210

p = \frac{2 \pm 2 10}{2}

Separate the equation into 2 possible cases

p = \frac{2 + 2 10}{2} p = \frac{2 - 2 10}{2}

Simplify the expression

More Steps

Evaluate

p = \frac{2 + 2 10}{2}

Divide the terms

More Steps

Evaluate

\frac{2 + 2 10}{2}

Rewrite the expression

\frac{2 ( 1 + 10 )}{2}

Reduce the fraction

1 + 10

p = 1 + 10

p = 1 + 10 p = \frac{2 - 2 10}{2}

Simplify the expression

More Steps

Evaluate

p = \frac{2 - 2 10}{2}

Divide the terms

More Steps

Evaluate

\frac{2 - 2 10}{2}

Rewrite the expression

\frac{2 ( 1 - 10 )}{2}

Reduce the fraction

1 - 10

p = 1 - 10

p = 1 + 10 p = 1 - 10

Solution

p_{1} = 1 - 10, p_{2} = 1 + 10

Alternative Form

p_{1} \approx - 2.162278, p_{2} \approx 4.162278

Show Solution