Question

Consider the quadratic equation x2 + 2x - 35 = 0. Solve by factoring and using the zero-product property.

Answer 1

Answer:

x = -7

x = 5

Step-by-step explanation:

The standard form of quadratic equations is

Ax^2 + Bx + C = 0

The factors need to multiply together to be C and add together to be B.

The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.

The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.

x + 7 = 0

-7 -7 Subtract 7 from each side to solve

x = -7

x - 5 = 0

+5 +5 Add 5 to each side to solve

x = 5

Answer 2

Quadratic equations

To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.

a + b = 2

ab = −35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.

• −1.35
• −5.7

Calculate the sum of each pair.

• −1 + 35 = 34
• −5 + 7 = 2

The solution is the pair that gives sum 2.

• a = −5
• b = 7

Rewrite the factored expression (x + a)(x + b) with the values obtained.

• (x − 5)(x + 7)

To find solutions to equations, solve x−5=0 and x+7=0.

• x = 5
• x = −7

What are the solutions of quadratic equations called?

• The "solutions" of a Quadratic Equation are the values where the equation equals zero. They are also called "roots", or even "zeros".

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