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

y = x2 – 3x – 10

roots are x intercepts on form of (x,0)
Let's solve the quadratic equation
y = x2 – 3x – 10
(x-5)(x+2)
x=5,-2
roots: (5,0)(-2,0)
let's see of these are correct
y = x2 – 3x – 10
y=(5)^2-3 (5)-10
y=25-15-10
y=10-10
y=0

y = x2 – 3x – 10
y=(-2)^2-3 (-2)-10
y=4+6-10
y=10-10
y=0

the roots are correct

Answer Link

ap8997154 ap8997154 · Answer 2 · 2022-02-19T10:04:30+01:00

Quadratic equation can be written in the form ax²+bx+c. The roots of the quadratic equation [tex]y = x^2-3x-10[/tex]-2 and 5.

What is a Quadratic Equation?

A quadratic equation is an equation that can be written in the form of

ax²+bx+c.

Where a is the leading coefficient, and

c is the constant.

How to find replace the mid-value of a quadratic equation?

To find the roots of the given quadratic equation we will find two numbers whose sum is equal to -3 and the product is equal to -10 to replace -3 in the given quadratic equation.

Given to us[tex]y = x^2-3x-10[/tex]

The quadratic equation can be written as,

[tex]\begin{aligned}y&=x^2-3x-10\\&=x^2-5x+2x-10\end{aligned}[/tex]

Taking x common from the first two terms while 2 as common from the last two terms,

[tex]=x^2-5x+2x-10\\\\=x(x-5)+2(x-5)\\\\= (x+2)(x-5)[/tex]

equating the two factors we get against zero,

(x+2) = 0

x = -2

(x-5) =0

x =5

Hence, the factors of the given quadratic equation are -2 and 5.

Learn more about Quadratic equations:

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