To find the quadratic polynomial, we can use the fact that the zeroes of the polynomial are given as 2 and -3.

Step 1: Recall that the zeroes of a quadratic polynomial are the values of x for which the polynomial equals zero. In this case, the zeroes are 2 and -3.

Step 2: We can use the fact that the sum of the zeroes of a quadratic polynomial is equal to the opposite of the coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the sum of the zeroes is 2 + (-3) = -1.

Step 3: We can also use the fact that the product of the zeroes of a quadratic polynomial is equal to the constant term divided by the coefficient of the quadratic term. In this case, the product of the zeroes is 2 * (-3) = -6.

Step 4: Now, let's write the quadratic polynomial in the form ax^2 + bx + c. We know that the sum of the zeroes is -1, so the coefficient of the linear term (a + 1) must be -1. Therefore, a + 1 = -1, which implies a = -2.

Step 5: We also know that the product of the zeroes is -6, so the constant term b must be -6.

Step 6: Putting it all together, the quadratic polynomial is x^2 + (-2 + 1)x - 6, which simplifies to x^2 - x - 6.

Question

To find the quadratic polynomial, we can use the fact that the zeroes of the polynomial are given as 2 and -3.

Step 1: Recall that the zeroes of a quadratic polynomial are the values of x for which the polynomial equals zero. In this case, the zeroes are 2 and -3.

Step 2: We can use the fact that the sum of the zeroes of a quadratic polynomial is equal to the opposite of the coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the sum of the zeroes is 2 + (-3) = -1.

Step 3: We can also use the fact that the product of the zeroes of a quadratic polynomial is equal to the constant term divided by the coefficient of the quadratic term. In this case, the product of the zeroes is 2 * (-3) = -6.

Step 4: Now, let's write the quadratic polynomial in the form ax^2 + bx + c. We know that the sum of the zeroes is -1, so the coefficient of the linear term (a + 1) must be -1. Therefore, a + 1 = -1, which implies a = -2.

Step 5: We also know that the product of the zeroes is -6, so the constant term b must be -6.

Step 6: Putting it all together, the quadratic polynomial is x^2 + (-2 + 1)x - 6, which simplifies to x^2 - x - 6.

Knowee AI · Accepted Answer

To find the quadratic polynomial, we can use the fact that the zeroes of the polynomial are given as 2 and -3.

Step 1: Recall that the zeroes of a quadratic polynomial are the values of x for which the polynomial equals zero. In this case, the zeroes are 2 and -3.

Step 2: We can use the fact that the sum of the zeroes of a quadratic polynomial is equal to the opposite of the coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the sum of the zeroes is 2 + (-3) = -1.

Step 3: We can also use the fact that the product of the zeroes of a quadratic polynomial is equal to the constant term divided by the coefficient of the quadratic term. In this case, the product of the zeroes is 2 * (-3) = -6.

Step 4: Now, let's write the quadratic polynomial in the form ax^2 + bx + c. We know that the sum of the zeroes is -1, so the coefficient of the linear term (a + 1) must be -1. Therefore, a + 1 = -1, which implies a = -2.

Step 5: We also know that the product of the zeroes is -6, so the constant term b must be -6.

Step 6: Putting it all together, the quadratic polynomial is x^2 + (-2 + 1)x - 6, which simplifies to x^2 - x - 6.

If the zeroes of the quadratic polynomial x2 + (a + 1)x + b are 2 and -3, then

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