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

B. -2 and 5

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=(-b\pm √(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=(3\pm √((-3)^2-4* 1* (-10)))/(2* 1)\\\\x=(3\pm √(9+40))/(2)\\\\x=(3\pm √(49))/(2)\\\\x=(3\pm 7)/(2)\\\\x=(3+7)/(2),\ x=(3-7)/(2)\\\\x=(10)/(2),\ x=(-4)/(2)\\\\x=5,\ x=-2`

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

So, option B is correct.