Question

solve by factor

4x^2+11x-3=0

Answer 1

[AI-generated answer — Bot GPT 3.5]

We can factor the quadratic equation 4x^2 + 11x - 3 by finding two numbers that multiply to the product of the coefficient of x^2 (4) and the constant term (-3) and add up to the coefficient of x (11).

The product of 4 and -3 is -12, and the two numbers that multiply to -12 and add up to 11 are 12 and -1.

Therefore, we rewrite the middle term using these two numbers:
4x^2 + 12x - x - 3 = 0

Factor by grouping:
4x(x + 3) - 1(x + 3) = 0

Factor out the common factor of (x + 3):
(x + 3)(4x - 1) = 0

So, the factored form of the equation 4x^2 + 11x - 3 = 0 is:
(x + 3)(4x - 1) = 0

This gives us two possible solutions:
x + 3 = 0 -> x = -3
4x - 1 = 0 -> x = 1/4

Therefore, the solutions to the equation are x = -3 and x = 1/4.