Question

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

Answer 1

Answer: $x=-\frac{5}{4}$ and $x=-2$

Step-by-step 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

$x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}$