Question

1. for which of the following quadratic equations are the roots 2 and 5?

a. $x^2 - 3x - 10 = 0$

b. $x^2 + 7x - 10 = 0$

c. $x^2 - 11x - 10 = 0$

d. $x^2 - 7x + 10 = 0$

Explanation:

Step1: Recall root-to-quadratic formula

If roots are $r_1$ and $r_2$, equation is $(x-r_1)(x-r_2)=0$.

Step2: Substitute roots 2 and 5

$(x-2)(x-5)=0$

Step3: Expand the expression

$x^2 -5x -2x + 10 = 0$

Step4: Simplify the equation

$x^2 -7x +10 = 0$

Answer:

D. $x^2 -7x +10 = 0$