Question

What are the roots of y = x2 – 3x – 10?
–3 and –10
–2 and 5
2 and –5
3 and 10

Answer 1

The polynomial factors to (x - 5)(x + 2)
Set each factor = 0
x = 5, x = -2

Answer 2

Answer:

B. -2 and 5

Step-by-step explanation:

We are given the quadratic equation $y=x^2-3x-10$

The roots are given when we equate the polynomial to 0 i.e. $x^2-3x-10=0$

The roots of a quadratic equation $ax^2+bx+c=0$ is given by $x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$.

On comparing the equations, we have,

a= 1, b= -3 and c= -10

Substituting the values in the formula gives us,

$x=\dfrac{3\pm \sqrt{(-3)^2-4\times 1\times (-10)}}{2\times 1}\\\\x=\dfrac{3\pm \sqrt{9+40}}{2}\\\\x=\dfrac{3\pm \sqrt{49}}{2}\\\\x=\dfrac{3\pm 7}{2}\\\\x=\dfrac{3+7}{2},\ x=\dfrac{3-7}{2}\\\\x=\dfrac{10}{2},\ x=\dfrac{-4}{2}\\\\x=5,\ x=-2$

Thus, the roots of the equation are 5 and -2.

So, option B is correct.