To find the value of k in the quadratic polynomial x^2 - 2x + 15, we need to use the fact that the sum of the zeros is equal to 8. The zeros of a quadratic polynomial are the values of x that make the polynomial equal to zero.
In this case, let's assume the zeros are a and b. According to the given information, a + b = 8.
Now, we can use the sum and product of zeros formula. The sum of the zeros formula states that for a quadratic polynomial ax^2 + bx + c, the sum of the zeros is -b/a.
In our case, the sum of the zeros is -(-2)/1 = 2.
Since a + b = 8, and a + b = 2, we can conclude that a = 3 and b = 5.
Now, let's find the product of the zeros. The product of the zeros formula states that for a quadratic polynomial ax^2 + bx + c, the product of the zeros is c/a.
In our case, the product of the zeros is 15/1 = 15.
Since the product of the zeros is 15, and the zeros are 3 and 5, we can write the quadratic polynomial as (x - 3)(x - 5).
Expanding this, we get x^2 - 8x + 15.
Comparing this with the given quadratic polynomial x^2 - 2x + 15, we see that k = -8.
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Step-by-step explanation:
To find the value of k in the quadratic polynomial x^2 - 2x + 15, we need to use the fact that the sum of the zeros is equal to 8. The zeros of a quadratic polynomial are the values of x that make the polynomial equal to zero.
In this case, let's assume the zeros are a and b. According to the given information, a + b = 8.
Now, we can use the sum and product of zeros formula. The sum of the zeros formula states that for a quadratic polynomial ax^2 + bx + c, the sum of the zeros is -b/a.
In our case, the sum of the zeros is -(-2)/1 = 2.
Since a + b = 8, and a + b = 2, we can conclude that a = 3 and b = 5.
Now, let's find the product of the zeros. The product of the zeros formula states that for a quadratic polynomial ax^2 + bx + c, the product of the zeros is c/a.
In our case, the product of the zeros is 15/1 = 15.
Since the product of the zeros is 15, and the zeros are 3 and 5, we can write the quadratic polynomial as (x - 3)(x - 5).
Expanding this, we get x^2 - 8x + 15.
Comparing this with the given quadratic polynomial x^2 - 2x + 15, we see that k = -8.
So, the value of k is (d) 15.
Answer:
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