Determine the zero(s) of the quadratic function y=6x2+13x+5
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To find the zero(s) of the quadratic function y=6x^2+13x+5, we need to set y to 0 and solve for x.
0 = 6x^2 + 13x + 5
To simplify the equation, we can factor the quadratic or use the quadratic formula.
Using factoring, we need to find two numbers whose product is 5*6=30 and whose sum is 13. The numbers 10 and 3 satisfy these conditions.
0 = (2x + 1)(3x + 5)
Setting each factor equal to zero:
2x + 1 = 0
3x + 5 = 0
Solving for x:
2x = -1
x = -1/2
3x = -5
x = -5/3
Therefore, the zeros of the quadratic function y=6x^2+13x+5 are x = -1/2 and x = -5/3.
To determine the zero(s) of the quadratic function y = 6x^2 + 13x + 5, we need to find the values of x where the function equals zero.
Step 1: Set the function equal to zero:
6x^2 + 13x + 5 = 0
Step 2: Factor the quadratic equation:
To factor, we need to find two numbers that multiply to give 6 * 5 = 30 and add up to 13. The numbers 10 and 3 satisfy these conditions, so we can rewrite the quadratic equation as:
(2x + 5)(3x + 1) = 0
Step 3: Set each factor equal to zero and solve for x:
Setting 2x + 5 = 0 gives:
2x = -5
x = -5/2
Setting 3x + 1 = 0 gives:
3x = -1
x = -1/3
Therefore, the zeros of the quadratic function y = 6x^2 + 13x + 5 are x = -5/2 and x = -1/3.
To determine the zeros of the quadratic function y = 6x^2 + 13x + 5, you need to find the values of x that make y equal to zero. In other words, you are looking for the x-values where the graph of the quadratic crosses the x-axis.
Here are the steps to find the zeros of the quadratic function:
Step 1: Set y = 0 and replace y in the quadratic equation with zero:
0 = 6x^2 + 13x + 5
Step 2: Factorize the quadratic equation:
To factorize the quadratic equation, we need to find two binomials that multiply together to give 6x^2 + 13x + 5.
The factors will have the form:
(2x + )(3x + )
Now, we need to find the factors of 5 that can be combined to give 13. The factors of 5 are 1 and 5, and when combined, they give 6.
We can put 1 as the coefficient of 2x and 5 as the coefficient of 3x:
(2x + 1)(3x + 5)
Step 3: Set each factor equal to zero and solve for x:
2x + 1 = 0 => 2x = -1 => x = -1/2
3x + 5 = 0 => 3x = -5 => x = -5/3
Therefore, the zeros of the quadratic function y = 6x^2 + 13x + 5 are x = -1/2 and x = -5/3.