Quadratic Equations Problem 2 | Algebra 1 | SAT Math Practice

Determine the roots of the quadratic equation below as part of your SAT Math Prep:
x^2 - 7x + 12 = 0

Can we factor it? Look for the values of a and b such that:
a + b = 7

and:
a * b = 12

One solution is:
a = 4
b = 3

Because:
a + b = 4 + 3 = 7
a * b = 4 * 3 = 12

The factorization is:
(x - 4)(x - 3)

Expanding gives:
x^2 - 3x - 4x + 12

This simplifies to:
x^2 - 7x + 12

So given:
(x - 4)(x - 3)

We can apply the zero-product property. Set each factor to zero.

For x = 4, we get x - 4 = 0
And for x = 3, we get x - 3 = 0

Therefore, the roots of this quadratic equation are:
x1 = 4
x2 = 3

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