How do you solve 4x^2+17x+15=0?

3 Answers

x = -3 or x = -5/4

Explanation:

4x^2 + 17x+15=0

Do

4x^2+12x+5x+15=0

Then

4x(x+3)+5(x+3)=0

(4x+5)(x+3)=0

So

x =-3" " or " "x=-5/4

Jun 11, 2018

-3, and -5/4

Explanation:

Method 1. Use the improved quadratic formula
y = 4x^2 + 17x + 15 = 0.
D = d^2 = b^2 - 4ac = 289 - 240 = 49 --> d = +- 7
There are 2 real roots:
x = -b/(2a) +- d/(2a) = - 17/8 +- 7/8
x1 = -24/8 = - 3
x2 = -10/8 = -5/4
Method 2. Use the new Transforming Method (Socratic, Google Search)
Transformed equation: y' = x^2 + 17x + 60.
Proceeding. Find the 2 real roots of y', then, divide them by a = 4.
Find 2 real roots, bot negative (Rule of signs), knowing the sum (-b = -17), and the product (ac = 60). They are - 5 and - 12.
The 2 real roots of y are:
x1 = -5/a = -5/4, and x2 = -12/a = -12/4 = -3

Jun 11, 2018

x-3 or x = -5/4

Explanation:

Factorise the quadratic trinomial.

Find factors of 4 and 15 whose products add to 17

" "4 and 15
" "darr" "darr
" "4" "5" "rarr 1 xx 5 =5
" "1" "3" "rarr 4xx3 = ul12
color(white)(xxxxxxxxxxxxxxxxx)17

The signs are all positive.

(4x+5)(x+3)=0

Either factor can be equal to 0

If 4x+5=0" "rarr x =-5/4

If x+3=0" "rarr x =-3