Question

Solve the quadratic function by factoring.
y = 4x² 13x + 10

Answer 1

Answer:
`x=-(5)/(4)` and
`x=-2`

Explanation:

To factor an equation in the form of
`ax^2+bx+c` you need to find the value of
`ac`. So first solve for that

`(4)(10) = 40`

Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40

Now split 13x into 5x+8x and solve by grouping

`4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)`

Factor out the GCF in each quantity

`(4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)`

Now group x+2 together

`(x+2)(4x+5)`

Finally, set each factor equal to 0 and solve for x

`x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\(4x)/(4) =(-5)/(4) \\x=-(5)/(4)`