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?
By BYJU'S Exam Prep
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
Answer:
If the zeroes of the quadratic polynomial x² + (a + 1) x + b are 2 and -3, then the values of a = 0 and b = -6
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