Have 2 questions:
1. Factor Trinomial competely
x^2 + 8x + 53 (reads as x squared plus 8x plus 53) I am thinking it is prime.
2. Solve
4x^2 + 23x - 30=0
(reads 4x squared plus 23x minus 30 equals zero
Factoring a quadratic and solving the corresponding quadratic equation are closely related.
in the first case I would consider solving it as
x^2 + 8x + 53 = 0
since the only factors of 53 are 1 and 53 itself, there is no way we can get that 8 in the middle.
using the formula we get imaginary roots, so the thing does not factor.
2.
4x^2 + 23x - 30 = 0
just use the quadratic formula,
I got x = (-23 ± √1009)/8
we haven't used the quadratic formula yet. for #2 i m trying to find the factors of 30 that add to 23. not finding any..any idea
the second question reads as 40x squared plus 23x minus 30=0
1. To factor the trinomial completely, we need to find two binomials that, when multiplied together, will give us the original trinomial. In this case, we have x^2 + 8x + 53.
To determine if the trinomial is prime (meaning it cannot be factored any further), we can check if it has any real roots. We can use the quadratic formula to find the roots:
x = (-b ± √(b^2 - 4ac)) / (2a)
Here, the coefficients of the trinomial are a = 1, b = 8, and c = 53.
Plugging in the values, we get:
x = (-8 ± √(8^2 - 4*1*53)) / (2*1)
x = (-8 ± √(64 - 212)) / 2
x = (-8 ± √(-148)) / 2
Since the discriminant (b^2 - 4ac) is negative, √(-148) is a complex number and there are no real roots. Therefore, the trinomial x^2 + 8x + 53 is indeed prime and cannot be factored further.
2. To solve the quadratic equation 4x^2 + 23x - 30 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Here, the coefficients of the equation are a = 4, b = 23, and c = -30.
Plugging in the values, we get:
x = (-23 ± √(23^2 - 4*4*(-30))) / (2*4)
x = (-23 ± √(529 + 480)) / 8
x = (-23 ± √(1009)) / 8
Since the discriminant (b^2 - 4ac) is positive and √(1009) is a real number, we can continue solving the equation.
So, the two possible solutions are:
x = (-23 + √(1009)) / 8
x = (-23 - √(1009)) / 8
These are the solutions to the quadratic equation 4x^2 + 23x - 30 = 0.