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10 grade maths

How do you factor and solve x² - 8x + 15 = 0?

Aniket Singh

11 Months agoGrade

1 Answer

Askiitians Tutor Team

Approved Tutor Answer11 Months ago

To factor and solve the quadratic equation x² - 8x + 15 = 0, follow these steps:

Step 1: Identify the Coefficients

In the equation, the coefficients are:

a (coefficient of x²) = 1
b (coefficient of x) = -8
c (constant term) = 15

Step 2: Find Two Numbers

Look for two numbers that multiply to c (15) and add up to b (-8). The numbers are:

-3 and -5

Step 3: Write the Factored Form

Using these numbers, you can express the quadratic as:

(x - 3)(x - 5) = 0

Step 4: Solve for x

Set each factor equal to zero:

x - 3 = 0 → x = 3

x - 5 = 0 → x = 5

Final Solutions

The solutions to the equation x² - 8x + 15 = 0 are:

x = 3

x = 5

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