Question

1. what are the real roots of $x^2 - 7x + 10 = 0$?

a 2 and 5
b 1 and 10
c -1 and -10
d -2 and -5

Explanation:

Step1: Factor the quadratic equation

We need to factor \(x^2 - 7x + 10 = 0\). We look for two numbers that multiply to \(10\) and add up to \(-7\) (the coefficient of \(x\) with a sign change because of the factoring form \((x - a)(x - b)=x^2-(a + b)x+ab\)). The numbers are \(-2\) and \(-5\) because \((-2)\times(-5)=10\) and \(-2+(-5)=-7\). So the factored form is \((x - 2)(x - 5)=0\).

Step2: Solve for \(x\)

Set each factor equal to zero:

• For \(x - 2 = 0\), we get \(x = 2\).
• For \(x - 5 = 0\), we get \(x = 5\).

Answer:

A. 2 and 5