  # If the Zeros of the Quadratic Polynomial x² + (a + 1) x + b are 2 and -3, Then What are the Values of a and b?

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Updated on: October 17th, 2023 If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then
a. a = -7, b = -1
b. a = 5, b = -1
c. a = 2, b = -6
d. a = 0, b = -6

To find out the values of a and b, we will use the following steps:

• Step 1: Use the fact that the sum of the zeros of a quadratic polynomial is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term.
• Step 2: Simplify the equation
• Step 3: Solve for a
• Step 4: Use the fact that the product of the zeros of a quadratic polynomial is equal to the constant term divided by the coefficient of the quadratic term.

Table of content ## If the Zeros of the Quadratic Polynomial x² + (a + 1) x + b are 2 and -3, Then What are the Values of a and b?

Solution:

If the zeros of the quadratic polynomial x² + (a + 1)x + b are 2 and -3, we can use Vieta’s formulas to relate the coefficients of the polynomial to its zeros.

Vieta’s formulas state that for a quadratic polynomial ax^2 + bx + c = 0 with zeros p and q, the following relationships hold:

p + q = -b/a pq = c/a

In our case, the zeros are 2 and -3. Therefore, we have the following equations:

2 + (-3) = -(a + 1)/1 2(-3) = b/1

Simplifying these equations:

-1 = -(a + 1) -6 = b

From the first equation, we can solve for a:

-1 = -(a + 1) 1 = a + 1 a = 1 – 1 a = 0

From the second equation, we can find the value of b:

-6 = b

Therefore, the values of a and b are: a = 0 b = -6 GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com